17. If 2 tana tan?ß tan?y + tan a tan-ß + tan B tany + tan?a tan?y 1 (a. B.y e R. a. B.y (2x+1) 5sin?o-Csino +3yino-3 Couo(che-iH 3(sh@-) where x is an integer) (A) sin?a + sin?B + sin2y 1 (B) cos2a + cos2B- cos2y 1 (C) cosa + cos B + cosy 2 (D) cos(a + B) cos(a-B) = cosy %3D Sing=T. %3D (AC)

Q: 12 and x terminates in 13 nd sin 2x, cos 2x, and tan 2x if sin x= sin 2x cos 2x %3D tan 2x %3D II

A:

Q: 2 += cos 3t 3 -- sin 3t 4 3. L 20s? – 103s + 423 6. 28(s – 5)(s? – 9) 20s? – 103s – 423 20s2 + 103s…

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Q: If y= In(4 tan (4x) ), then y' tan(4x) = Select one: 04/(1+x² ) O None O 4/(1 + 16 x² ) 01/(1+ x² )…

A:

Q: 63. First, observe sin 4x = 2 sin 2x cos 2x = 2 sin 2.x(1 – 2 sin? x) = 2 sin 2x – 4 sin 2x sin² x =…

A:

Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

A:

Q: /2 1lf If In = " x cos" x dx, when n> 1, show that п(п — 1)1-2 — 1 In 12 [Hint: cos" x = cos²…

A: Given: In=∫0π2x cosnx dx

Q: d Select one: æ(sin=! æ)* 3x + 2 sin- x 3x x(sin x) -1 + 2(sin-1 x)? 1-a2 x² (sin-1 æ) 3(sin1 x) +…

A:

Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: Find sin 2x, cos 2x, and tan 2x if tanx= and x terminates in guadrant III. 3

A: To find the value of sin (2 x), cos (2 x), and tan (2 x).

Q: sin (+) can be expanded to: π TT O sin COS sin sin 4 7 TT O sin sin COS cos 4 T Osin COS + cos sin…

A: Solved below.

Q: 4 A. 1 B. 2 C. 3 D. 4 If the correct answer in (2) is equal to -, how many case/s is/are possible? 5…

A:

Q: Show that (cos 0 + i sin 0)" = cos n0+ i sinne for n = 3 and n = 4.

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: 57 where 2 tan 0 = <0 < 3T 3 Find sin 20 7 24 24 25 24 25 25 24 4,

A: By using sin(2x) formula in terms of tan(x).

Q: 9 If f(0) = cos 01 cos 02· cos 03 ... cos On + tan 0,}=- f (0) Show, {tan 0, + tan 02 + tan 03 +…

A:

Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3…

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts.…

Q: 1. If Y= 4 In (In (In(sec(x)) then Ý=[4 (tan)/{ In ((In (sec)) In (sex)}]

A:

Q: Stan 2xdx O-In(cos 2x) + C O-In (cos 2x) + C O-In (sin 2x) + C O tan² 2x 2 + C

A: INTEGRATION

Q: Find y' (or ) if In(21y) sin z = zy4 + 8z5 y5-yln(21y) cos z+40z4y sin z+4zy4 y5-yln(21y) cos…

A:

Q: 1 Suppose y = tan ¹æ. Then x = y tan Otan y Oarctan y

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Q: 9 sin sin 2O° =Y 1o) cos cos 70 = a4 24 1)Sin Sin 7o = X 24 12) cos cos 20 = _ x %3D 24 24 20

A:

Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

A:

Q: Evaluate: e* cos (7e*) cos (4e*) dx - sin (3e*) + –sin (11e*)+C A 22 B - sin (3e*) – –sin (11e*) +C…

A: Evaluation of the Integral

Q: - IF z = tan2 -1 y Show that x- ây

A:

Q: Compute / sin? æ dæ. sin 2x + C 4 sin a +C 3 cos 2x + C 4 2 sin 2x + C 4 cos 2x + C 4 2

A:

Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

Q: Let y = sin(sin(50)). Then y" is equal to: %3D Q7 -25 cos (50) sin(cos(50)) – 25 sin(50)…

A:

Q: 15 Find sin 2x, cos 2x, and tan 2x if sinx and x terminates in guadrant III. 17

A: Given that: sinx=−1517 To find: sin2x, cos2x, tan2x

Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

A:

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: Compute 4 sin(TTX) d dx A. 4 sin(TTX) B. 4sin(TTX) In4 C. 4sin(x) (πIn4).cos(TTX) D. 4 sin(TTX)…

A:

Q: 18. Evaluate fe³x cos 8x dx e3x a. [8sin 8x 3 cos 8x] + C 3x b. [8sin 8x + 3 cos 8x] + C 73 C. d.…

A:

Q: v3 V3 sin 30 = , cos 30° = , tan 30° = COS %3D O sin 30° = , cos 30° = . , tan 30° = %3D %3D V3, cos…

A:

Q: Let m be the number of solutions of sin (2x) + cos (2x) + cos x + 1 = 0 in 0<x< x< 1/1/2 and 7 7π n…

A: The roots of the equation: f(x)=0 are the values of x, where the graph of the function: y=f(x)…

Q: 1,1Y= 4 in (In (in(sec(x)) then Ý -14 (tan)! In ((In (sec)) In (sex);| O True O False

A: This is the question of the application of differential calculus.

Q: 4 Find sin 2x, cos 2x, and tan 2x if cosx= and x terminates in guadrant III.

A:

Q: 1 을 with If sin B B in Ql, find B sin ? В sin 3 + 2 6. 2 B sin 3 + 2 3+22 sin 2 6 sin 2 B 3+2/2

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Q: 4 Giren tan A =– where 0<AS Find 2sin 2A.

A:

Q: 5. Find when y-In () A. 2000)+ sin(x) B. In (()) 2² C. xoos (x) + sin (0 D. 2009 (3) sin(x) xsin (x)…

A: Given: y=lnsinxx   As we know that; The Chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2…

Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

A: Given: cos3y+sin2x=2x+3y To find dydx in the given equation.

Q: Q/ IF y = Sim ܠܐ 10²² (4) y = 3/² sin(x) cos(x) Prove that

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

A:

Q: S(32+2*)sin(z)dz 3z +

A: In this question we have to solve Integration.

Q: Prove that : A) sin(h3x) =3sin(hx)+4sin(h³ n(n°x) B) 13 cos(hx) 3 C) 2tan(hx) tan(h2x) 1+ tan(h²x)

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Q: sec 0 + In + 27+3 = -3 2 In y? + 327 – 4 = 1+ cos 20 2/1+ (tan 0)² + 2ln /y + 22 = -3

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Q: (osh x- Sinn? 21 Sin nx=1 20 (Osh K= ?

A:

Q: 3. If tan(a-iß) = x- iy , show that x? + y?-2ycoth2B = -1

A:

Q: 14. If we let u = 4x – 1 for the s²tan(4x-1)-3 cos"(4x-1) dx. what will be the cos(4x-1) resulting…

A: This is a integration problem