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SHEET 20 TRIGONOMETRIY (COLLECTION # 1)Single Correct Typecos A cos C cos(A B) cos(B C)Que. 1. If A B C 180o then cos A sin C sin(A B)cos(B C) simplifies to(a) cot C(b) 0(c) tan C(d) cot C(code-V1T2PAQ2)Que. 2 Let 3a 4, 4b 5,5c 6, 6d 7, 7e 8 and 8f 9. The value of product (abcdef), is(a) 1(b) 2(c)6(d) 3(code-V1T2PAQ3)(d) cos ec15o(code-V1T2PAQ4)Que. 3. Which of the following numbers is the largest ?(a) cos15ο(c) sec15o(b) tan 60 osin α sin γQue. 4. If α γ 2β then the expressionsimplifies tocos γ cos α(a) tan β(b) tan βQue. 5. If A 110o then(a) tan A(code-V1T2PAQ6)(c) cot β(d) cot β(c) cot A(d) – cot A(code-V1T4PAQ2)(d) 776(code-V1T4PAQ4)1 1 tan 2 2Aequalstan 2A(b) – tan BQue. 6. Minimum value of y 256sin 2 x 324 cos ec2 x x R is(a) 432(b) 504Que. 7. If A 320o then(a) tanA2 1 1 tan 2 Ais equal totan A(b) tan (c) 580x A2(code-V1T5PAQ1)(c) cotx x A2(d) cotA2x Que. 8. The product cos . cos . cos . cos is equal to248256sin x(a)128sinx256(b)sin x256sinx256 sin x(c)128sinx128(d)(code-V1T5PAQ3)sin x512sinx512Que. 9. In a triangle ABC A 60o , B 40o and C 80o. If P is the centre of the circumcircle of triangle ABC with radius unity, then the radius of the circumcircle of triangle BPC is (code-V1T5PAQ5)(a) 1(b) 3(c) 2(d) 3 2Que. 10. In a triangle ABC if angle C is 90o and area of triangle is 30, then the minimum possible value ofthe hypotenuse c is equal to(code-V1T5PAQ9)(a) 30 2(b) 60 2(c) 120 2Que. 11. Which one of the following relations does not hold good ?(a) sinπ13π1sin 10104(c) 4 ( sin 24o cos 6o ) 15 3(b) sin(d) 2 30(code-V1T5PAQ13)π13π1 sin 10102(d) sin 2 72o sin 2 60o 5 14Address : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 1 of A - 34
Que.12. With usual notations, in a triangle ABC, a cos ( B C ) b cos ( C A ) c cos ( A B ) is equal to(a)abcR2abc4R 2(b)(c)4abcR2(d)abc2R 2(code-V1T5PAQ15)Que. 13. General solution of the equation, 2sin 2 x sin 2 2x 2, is(a) ( 2n 1)π4(b) nπ π4(c) nπ π2(code-V1T5PAQ16)π4(d) nπ nπ π2Que. 14. In a triangle ABC, A 60o and b : c 3 1: 2 then ( B C ) has the value equal to(a) 15o(b) 30o(c) 22.5o(d) 45O(code-V1T5PAQ17)Que. 15. If the two roots of the equation, x 3 px 2 qx r 0 are equal in magnitude but opposite sign then(a) pr q(b) qr p2Que. 16. The equation, sin θ (a) no root(c) pq r(d) pq r 044 1 3hassin θ 1sin θ 1(code-V1T5PAQ20)2(b) one root(c) two roots(code-V1T5PAQ18)(d) infinite rootsa 2 b2 c2lies in the intervalQue. 17. If a,b,c are the sides of a triangle then the expressionab bc ca(a) (1,2)(b) [1,2](c) [1,2)(d) (1,2](code-V1T5PAQ23)Que. 18. If α and β are the roots of the equation a cos 2θ bsin 2θ c then cos 2 α cos 2 β is equal to(a)a 2 ac b 2a 2 b2(b)a 2 ac b 2a 2 b2(c)2b 2a 2 c2(d)2a 2b2 c2bQue. 19. If tan θ , then the value of a cos 2θ b sin 2θ is equal toa(a) a(b) bQue. 20. Let f k ( x ) (a)(b)2Que. 21. In a triangle ABC, cosr2R(code-V1T7PAQ5)(d) a 2 bsin k x cos k xthen f 4 (x) f 6 (x) is equal tok1 1 cos 2 2x4 6(a) 2 (c) ab 21 1 2 sin 2x12 4(c)1 1 cos 2 x3 4(code-V1T7PAQ6)(d)112ABC cos 2 cos 2 equal222(b) 4 7r2R(c) 2 (code-V1T5PAQ24)r4R(code-V1T7PAQ7)(d)3 4r 1 4 R where r and R have their usual meaning.Que. 22. A cricle is inscribed in a triangle ABC touches the side AB at D such that AD 5 and BD 5 and BD 3. If A 60o then the length of BC equals [Advise - Que. of properties of triangle but tru by 2D.](a) 9(b)12013(c) 12(d) 13(code-V1T7PAQ8)Address : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 2 of A - 34
Que. 23. If in a trianlge ABC, sin A, sin B, sin C are in A.P., then(code-V1T7PAQ10)(a) The altitudes are A.P.(b) The altitudes are in H.P(c) The medians are in G.P.(d) The medians are in A.P.Que. 24. Which of the following inequalitie(s) hold(s) true in any triangle ABC ?(code-V1T7PAQ13)(a) sinABC 1sin sin 222 82(c) sin(b) cosA 2B 2C 3sinsin 222 4Que. 25. If α ABC 3 3cos cos 22282(d) cosABC 9 cos 2 cos 2 222 4πwhich of the following hold(s) good ?7(code-V1T7PAQ14)(a) tan α.tan 2α.tan 3α tan 3α tan 2α tan α(b) cos ec α cos ec 2α cos ec 4α(c) cos α cos 2α cos3α has the value equal to 1/2(d) 8cos α.cos 2α.cos 4α has the value equal to 1.Que. 26. Identify which of the following are correct ?(a) ( tan x ) n ( sin x ) ( cot x ) n ( sin x )(code-V1T7PAQ16) π , x 0, 4 π(b) 4 n cosec x 5 n cosec x, x 0, 2 1 (c) 2 n ( cos x ) 1 3 n ( cos x ) π , x 0, 2 (d) 2 n ( tan x ) 2 n (sin x ) , x 0, π 2 Que. 27. Which of the following is always equal to cos 2 A sin 2 A ?(code-V1T10PAQ4)(a) sin 2A(b) cos ( A B ) cos ( A B) sin ( A B ) sin ( A B)(c) sin ( A B ) cos ( A B) cos ( A B ) sin ( A B)(d) cos ( A B ) sin ( A B) sin ( A B ) cos ( A B)Que. 28. Number of values of x [ 0, π] satisfying cos 2 5x cos 2 x sin 4x.sin 6x 0, is(code-V1T10PAQ5)(a) 2(b) 3(c) 5(d) infinitely manysin α sin β sin ( α β )Que. 29. sin α sin β sin α β (wherever difined) simplifies to()(a) cotαβcot22(b) cotαβtan22(c) tanαβcot22(code-V1T10PAQ6)(d) tanαβtan22Address : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 3 of A - 34
Que. 30. Let A, B, C be three angles such that A B C π. If tan A. tan B csccos A cos Bπthen the vlaue ofcos C6is equal to12(a)(code-V1T12PAQ5)13(b)(c) 1(d)12Que. 31. Which value of θ listed below leads to 2sin θ 1 and 3cos θ 1 ?(a) 70o(b) 140o(c) 210o(code-V1T12PAQ7)(d) 280oQue.32. In a trinalge ABC, a 3, b 4 and c 5. The value of sin A sin 2B sin 3C equals(a)24251425(b)(c)6425(d) None.(code-V1T13PAQ1)Que.33. Let y ( sin x cos ecx ) ( cos x sec x ) , then the minimum value of y,, x R is2(a) 72(b) 8(c) 9(code-V1T13PAQ4)(d) 10Que.34. If the equation cot 4 x 2 cosec 2 x a 2 0 has atleast one solution then, sum of all possible integralvalues of ‘a’ is equal to(code-V1T13PAQ5)(a) 4(b) 3(c) 2(d) 0Que.35. If θ be an acute angle satistying the equation 8cos 2θ 8sec 2θ 65, then value of cos θ is equal to(a)18(b)23(c)2 33(d)34Que.36. If 2sin x 7 cos px 9 has atleast one solution then p must be(code-V1T13PAQ8)(a) an odd integer(b) an even integer(c) a rational number(d) an irrational numberQue.37. If θ ( π / 4, π / 2 ) and n 1(a ) 31 tannθ sin θ cos θ then the value of tan θ is(b) 2 1(c) 2 3(b) a 2 b 2 1(c)a 2 b2 1(code-V1T13PAQ11)(d) a 2 b2 1Que.39. The least value of x for 0 x π / 2, such that cos(2x) 3 sin(2x), is(a)π12(b)2π12(c)3π12(code-V1T13PAQ10)(d) 2Que.38. If sin x a cos x b then the value of a sin x cos x is equal to(a) a 2 b 2 1(code-V1T13PAQ7)(d)(code-V1T13PAQ14)4π12Que.40. Let θ [ 0, 4π] satisfying the equation ( sin θ 2 )( sin θ 3)( sin θ 4 ) 6. if the sum of all value of θis of the form kπ then the value of ‘k’, is(code-V1T13PAQ18)(a) 6(b) 5(c) 4(d) 2Que.41. Let f (x) a sin x c, where a and c are real numbers and a 0. Then f (x) 0 x R if(a) c a(b) c a(c) a c a(d) c a(code-V1T13PAQ19)Address : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 4 of A - 34
Que.42. In which one of the following intervals the inequality, sin x cos x tan x cot x can hold good ? π 3π 5π 3π (b) , π 4 (a) 0, 4 7π (d) , 2π 4 (c) , 4 2 (code-V1T13PAQ21)Que.43. If sin x sin y sin z 0 cos x cos y cos z then the expression, cos ( θ x ) cos ( θ y ) cos ( θ z ) , for θ R is(code-V1T15PAQ1)(a) independent of θ but dependent on x, y, z(b) dependent on θ but independent of x, y, z(c) dependent on x, y, z and θ(d) independent of x, y, z and θQue.44. In ABC, AB 1, BC 1 and AC 1 2. In MNP, MN 1, and MNP 2 ABC. The side MPequals(b) 7 4(a) 3 29Que.45. The sum sinn 12(c) 2 2(d) 7 2nπequals18(a) 5(code-V1T15PAQ6)(b) 4Que.46. Let area of a triangle ABC is(code-V1T15PAQ5)(c)()5 13 1, b 2 and c 2((d) 3 5)3 1 and A is acute. The measure of theangle C is(code-V1T15PAQ10)(a) 15o(b) 30o(c) 60o(d) 75oQue.47. If the inequality sin 2 x a cos x a 2 1 cos x holds for any x R then the largest negative intergralvalue of ‘a’ is(code-V1T18PAQ2)(a) – 4(b) – 3(c) – 2 a 1(d) – 1 nQue. 48. The value of the expression sin . cos ( ka ) , is 2 2 k 1 11 sin n a 2 2 (a) 1 sin n 1 a (b)(c) sin ( ( n 1) a )(b) cos n ( a )2 2 (code-V1T18PAQ3)Que. 49. Suppose ABC is a triangle with 3 acute angle A,B and C. The point whose coordinates are( cos B sin A,sin B cos A ) can be in the(code-V1T18PAQ4)(a) first and 2nd quadrant(b) second the 3rd quadrant(c) third and 4th quadrant(d) second quadrant onlyQue. 50. Number of solution of the equation, sin 4 x cos 2 x sin x 2sin 2 x sin x 0 is 0 x 3π, is(a) 3(b) 4(c) 5(d) 6(code-V1T19PAQ3)Address : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 5 of A - 34
Que. 51. Let α, β and γ be the angles of a triangle with 0 α ππand 0 β , satisfying22sin 2 α sin 2 β sin γ, then(a) γ ( 0,30ο )(code-V1T20PAQ3)(b) γ ( 30ο , 60o )(c) γ ( 60ο ,90o )(d) γ 90oQue. 52. Let L and M be the respective intersections of the internal and external angle bisectors of thetriangle ABC at C and the side AB produced. If CL CM, then the value of ( a 2 b 2 ) is (where a & bhave their usual meanings)(a) 2R2(code-V2T1PAQ4)(b) 2 2 R 2(c) 4R 2(d) 4 2 R 2Que. 53. In a triangle ABC, if A B 120o and R 8r where R and r have their usual meaning then cos Cequals(a) 3/4(b) 2/3(c) 5/6(d) 7/8(code-V2T3PAQ9)Que. 54. The system of equations(code-V2T5PAQ13)x y cos θ z cos 2θ 0 x cos θ y z cos θ 0.x cos 2θ y cos θ z 0has non trivial solution for θ equals(b) nπ (a) nπ only, n I.(c) ( 2n 1) πonly, n I.21πonly, n I.4(d) all value of θ111 a 1 tan 1 tan 1 tan 1 is expressed as a rationalQue. 55. If tan tanin lowest form ( a b ) hasb2345 the value equal to(code-V2T8PAQ1)(a) 19(b) 27(c) 38(d) 45Que. 56. A sector OABO of central angle θ is constructed in a circle with centre O and of radius 6. Theradius of the circle that is circumscribed about the triangle OAB, is(code-V2T8PAQ7)(a) 6 cosθ2(b) 6 secθ2 θ (c) 3 cos 2 2(d) 3secθ2Que. 57. Let s, r, R respectively specify the semiperimeter, inradius and circumradius of a triangle ABC.Then ( ab bc ca ) in terms of s, r and R given by(a) sr rR Rs(b) R 2 r 2 rs(c) s 2 R 2 2rs(code-V2T8PAQ8)(d) r 2 s 2 4RrQue. 58. The value of the expression (1 tan A )(1 tan B ) when A 20o and B 25o reduces to(a) prime number(b) composite number(c) irrational number(d) rational which is not an integer.(code-V2T13PAQ5)Address : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 6 of A - 34
Que. 59. The least value of the expression(a) 1(b) 2cot 2x tan 2x π in 0, equals8 5π 1 sin 8x 2 (c) 4(code-V2T13PAQ11)(d) none.Que. 60. The value of x satisfying the equation sin ( tan 1 x ) cos ( cos 1 (x 1) ) is(a)12(b) 12(c)(code-V2T13PAQ22)(d) No finite value2 1Que. 61. Which one of the following quantities is negative ?(code-V2T13PAQ23)(a) cos ( tan 1 (tan 4) ) (b) sin ( cot 1 (cot 4) ) (c) tan ( cos 1 (cos 5) ) (d) cot ( sin 1 (sin 4) )Que. 62. The product of all real values of x satisfying the equation 2x 2 10 x 4 2 81 xsin 1 cos 2 cot cot 1 x 5 x 3 9x (a) 9(b) – 9(code-V2T13PAQ29) π is 2(c) – 3(d) – 1 2π 1 x 1Que. 63. Product of all the solution of the equation tan 1 2x, is cot 2 x 1 2x 3(a) 1(b) –1(c) 3(a) 1a b c d where a, b, c, d N andadis equal tobc(b) 2(code-V2T14PAQ4)(d) 3Que. 64. If the value of tan ( 37.5o ) can be expressed as( a b c d ) then the value of2(code-V2T14PAQ13)(c) 3(d) 4Que. 65. If the minimum value of expression y ( 27 )cos x ( 81)sin xcan be expressed in the formwhere a, b N and are in their lowest term then the value of ( a b ) equalsa/b(code-V2T17PAQ10)Que. 66. Let f (x) sin x cos x tan x arc sin x arc cos x arc tan x. If M and m are maximum and minimum values of f(x) then their arithmetic mean is equal to(code-V2T18PAQ3)(a)π cos12(b)π sin12(c)π tan1 cos14(d)π tan1 sin14Que. 67. The sum cos rπ equals2009r 1(a) 03π Que. 68. tan 8 (code-V2T19PAQ1) 6 (b) 120093π cot 8 (c)3 12 2(d)2 322009is(a) even integer(c) rational which is not an integer(code-V2T19PAQ3)(b) odd integer(d) irraionalAddress : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 7 of A - 34
Comprehesion Type# 1 Paragraph for Q. 1 to Q. 3Let r and R denote the radii of the incircle and the circumcircle of the triangle ABC with sides a, b, cand a b c 2s. Also denotes the area of the trianlge.(code-V1T16PAQ7,8,9)1.The value of the productA cot 2equalscyclicABC (b) 2sr2(a) 2.The vlaue of the sumR (a b c)(c)AB cot 2 cot 22abc(d)rs(d)4RrequalscyclicA,B,C(a)3.R 4rr(b)4R rr4R rR(c)Let f (x) 0 denotes a cubic whose roots are cotABC, cot , cot . If the triangle ABC is such that one222of its anlge is 90o then which one of the following holds good ?(a) r 2R s(b) 3r 2R s 2(c) 1 r 4R 2s(d) 4r R s# 2 Paragraph for Q. 4 to Q. 6Let ABC be an acute triangle with orthocenter H.D,E,F are the feet of the perpendiculars from A,B,andC on the opposite sides. Also R is the circumradius of the triangle ABC.(code-V1T18PAQ6,7,8)Given ( AH )( BH )( CH ) 3 and ( AH ) ( BH ) ( CH ) 724.The ratio(a)5.2314R2has the value equal to(b)37R(c)73R(d)143RThe product ( HD )( HE )( HF ) has the value equal to(a)6. cos A cos A2964R 3(b)98R 3(c)89R 3(d)932R 3(c)32(d)52The value of R is(a) 1(b) 31/ 3Address : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 8 of A - 34
Assertion & Reason TypeIn this section each que. contains STATEMENT-1 (Assertion) & STATEMENT-2(Reason).Eachquestion has 4 choices (A), (B), (C) and (D), out of which only one is correct.Bubble (A) STATEMENT-1 is true, STATEMENT-2 is True; STATEMENT-2 is a correctexplanation for STATEMENT-1.Bubble (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correctexplanation for STATEMENT-1.Bubble (C) STATEMENT-1 is True, STATEMENT-2 is False.Bubble (D) STATEMENT-1 is False, STATEMENT-2 is True.Que. 1. Statement - 1 :(code-V1T4PAQ8)In a triangle ABC if A is obtuse then tan B tan C 1becauseStatement - 2 :In any triangle ABC, tan A tan B tan Ctan B tan C 1Que. 2. Statement - 1 :(code-V1T4PAQ9)cos (10 ) and cos ( 10 ) both are negative and have the same value.ccbecauseStatement - 2 :cos θ cos ( θ ) and the real numbers (10 ) and ( 10 ) both lie in the third quadrant.ccQue. 3. Let α, β and γ satisfy 0 α β γ 2π and cos ( x α ) cos ( x β) cos ( x γ ) 0 x Rγ α Statement - 1 :2π.3(code-V1T6PAQ1)becausecos α cos β cos γ 0 and sin α sin β sin γ 0.Statement - 2 :Que. 4. If A B C π thenStatement - 1 :(code-V1T6PAQ3)cos 2 A cos 2 B cos 2 C has its minimum value3.4becauseStatement - 2 :18Maximum value of cos A cos Bcos C .Que. 5. Let f (x) 3sin 2 x 4sin x cos x 4 cos 2 x, x R.Statement - 1 :Greatest and least values of f (x) x R are(code-V1T8PAQ11)7 177 17andrespectively.22becauseStatemtnt 2 :a b a 2 b 2 c2 2aba b a 2 b 2 c 2 2ab a sin 2 x b sin x cos x c cos 2 x 22where a, b, c RAddress : Plot No. 27, III- Floor, Near Patidar Studio, Above Bond Classes, Zone-2, M.P. NAGAR, Bhopal“IITJEE MATHS BY SUHAG SIR” ON WWW.YOUTUBE .COMTeko Classes, Maths : Suhag R. Kariya (S. R. K. Sir), Bhopal Phone : 0 903 903 7779, 0 98930 58881.Also Available online www.MathsBySuhag.com DOWNLOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSES.COMIIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779Teko Classes www.TekoClasses.comQuestion. & Solution. Trigo. Page: A - 9 of A - 34
Que. 6. Statement - 1 :tan6π5ππ6π5ππ tan tan tan .tan . tan777777(code-V1T10PAQ7)becauseStatement - 2 :If θ α β, then tan θ tan α tan β tan θ.tan α.tan β.Que. 7. Consider the following statementsStatement - 1 :(code-V1T12PAQ8)In any right angled triangle ABC, sin 2 A sin 2 B sin 2 C 2becauseStatement - 2 :Que. 8. Statement-1: n cotIn any triangle ABC, sin 2 A sin 2 B sin 2 C 2 2 cos A cos B cos C ]InanytriangleABC n cot co t c o t 222 ABCABC n cot n cot222becauseStatement - 2 :Que. 9. Statement - 1 :(code-V1T14PAQ5)(( n 1 3 2 3)) n1 nGeneral solution of(3 n 2 3)tan 4x tan 2xnπ π 1 is x ,n I1 tan 4x tan 2x2 8becauseStatement - 2 :Que. 10. Statement - 1 :(code-V1T1
Teko Classes IIT JEE MATHS by SUHAG SIR Bhopal, Ph. 0 903 903 7779 www.TekoClasses.com Question. & Solution. Trigo. Page: A - 2 of A - 34 Also Available online www.MathsBySuhag.com DOWN LOAD FREE STUDY PACKAGE FROM WEBSITE WWW.TEKOCLASSE S.COM Teko
