3 sin(0 + 27) = 1 sin 0 cos O O - sin 0 2 sin 0 O sin 0 cos 0

Q: 2. Prove the identity: (cos x- sin x)2 + (cos x + sin x)2 = 2. %3D

A: To prove  that cosx-sinx2+cosx+sinx2=2

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A: This is the problem of complex analysis.

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A: Given: sinθ-cosθ+1sinθ+cosθ-1=sinθ+1cosθ

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A: Given that d(x3 sinx)/dx  . Here we derivative of this question with respect to x. We know that…

Q: (÷++) + co« (5 - ). cos 3 x ) is equivalent to O cos 2x cos x O sin x cos x

A:

Q: Solve ( sin θ - 2r cos^2 θ) dr + r cos θ ( 2r sin θ + 1) dθ = 0 a. r sin^2 θ - r^2 cos^2 θ = c b.…

A: Given that sinθ-2rcos2θdr+rcosθ(2rsinθ+1)dθ = 0. The objective is to solve the given equation.

Q: -sin 0 (b) 1 -sin 0| sin (0) – 1

A:

Q: (ii) Prove the identity (2 - 2 cos 0)(sin 0 + sin 20 + sin 30) -(cos 40 - 1) sin 0 + sin 40 (cos 0 –…

A: Prove the Identity: 2-2cosθsinθ+sin2θ+sin3θ=-cos4θ-1sinθ+sin4θcosθ-1 NOTE: Since you have asked…

Q: (cos(7+) +;cos(37x) +.) -1<x<0 7) S(x)=. 2r Ans. 0<x<1 2 sin(7 x) -sin(27 x) +

A:

Q: de (sin(0) cos(0)) =

A:

Q: 14. x" + y = -101 sin(10t) ; y " + x = 101 sin(10t) ; x(0) = 0, x ' (0) = 6, y(0) = 8, y' (0) = -6

A:

Q: -4 Evaluate /(cos' x sin x + cos x sin-6 Select one: a. -csc³ x + sin x + C b. -csc x + csc x + C С.…

A: Need to solve integration

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A: As we know, Sin2x + cos2 x = 1 Since the interval is not given so we have to find general solution

Q: sin 0 If 1+cos 0 x2 x2, then tan 2 - a) b) 4 c) x2 + 1 d) x2 |3| 2.

A: Given,  sin θ1+cos θ=x2 To determine tanθ2

Q: +sin(n")n-1 n6.1+cos(n2)n®+2 4. 2 9) Et sin (n* cos(n)

A: We have to use limit comparision test for checking divergence

Q: 65. 3 sin x = cos x 67. cosx- sin²x = 1 69. 2 cosx- 3 sin x- 3 = 70. 2 sin?x - cos x - 1 = C

A: 67. cos2x - sin2x =1 1 - 2sin²x = 1 Cos2x =1 2x = cos-(1) 2x = 0, 2π , 4π ..... x = 0,π,2π  So…

Q: sin(20) cos(20z) dæ- O 100 O 0 O -2 O 2

A:

Q: ƒ cos(x³) x² dx. 1 ¹ cos4 + c 4 1 WIT 3 1 -| sin x³+ C 1 ·cosª + c 4 4 -3 sin x³+ C

A: Topic = Integration

Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

A:

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: Find the limit.

A: Use the formula cosθ+ϕ=cosθ cosϕ-sinθsinϕ to simplify the term cosπ+∆x. Here θ=π and ϕ=∆x.…

Q: – 1) sin a cos a - sin æ 9(cos² e – 1) O 9 tanx + 9 sec a O 9 cot a + 9 cscx O 9 tana + 9 csc a O 9…

A:

Q: a) 2(sin x)? – 1 = 0 [0,27] b) 6(sin x)² + cos 2x + 1 = 0 [0,2n] c) (cos 2x)2 + cos 2x + 1 = 0 [- ,…

A: (a) ⇒2(sin(x))2-1=0⇒(2sin(x)-1)(2sin(x)+1)=0⇒sin(x)=12 OR sin(x)=-12⇒x=π4, 3π4 OR x=5π4, 7π4

Q: Cos 8 + sin 0 sin 0 1 cos 0 cos 8 sin e

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa.…

A:

Q: sin 3x + sin xr 3.2.1 = 2 sin x %3D 1+ cos 2x 3.2.2 sin 70 – sin 50° = sin 10 %3D Solve for x : 5tan…

A: The objective is to prove the given equations

Q: In Problems 28–44, establish each identity.

A: Trigonometric identities are given, we have to prove the identities. Note: we are answered with 3…

Q: 5 sin coso do 2 Sin ² + 3 sin 0 -4

A:

Q: 1- cos e sin 0 sin 0 1- cos 0 23.

A:

Q: 3 sin(0) + 5 cos(0)

A:

Q: 2 – 2 cos 2:r sin z sin z 1. cos z sin 2r 2. sin(a + B) sin(a – B) = sin² a – sin² 3 1- sin z' 1+…

A: Solution is here

Q: (sin 0 + cos 0)´ =1+ sin(20) s 0)° =1+sin(20)

A:

Q: Cos 9 2 Sin e cos8 © cos (e) cos o (d) cos'x + 2 Sinx + 2 = o

A:

Q: Ísin^2 (x) cos^2 (x) dx * O 1/8 x -1/32 sin4x + C O 1/8 x - 1/32 sinx + C O 1/8 -1/32 sinx + C O…

A:

Q: Cos 0–N1+ Sin 20 Tan 0 Sin 0 –/1 + Sin 20 N.

A: Recall: sin (2θ)= 2 sinθ cosθ sinθ cosθ= tanθ cos2θ+sin2θ=1

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A:

Q: 5 sin 0 – 4 cos 0 e of 5 sin 0 + 4 cos 0 is

A:

Q: 1+ sin 0 b) coso coso 1- sin 0

A:

Q: 1+ sin 0 cot e Prove : 1- sin 0 (cos ece – 1}

A: Given:                            1+sin θ1-sin θ=cot2θcosec θ-12 Solve left hand side:…

Q: 2 cos 2 ( x ) − 7 cos ( x ) + 5 = 0

A: Topic - trigonometric Equations Put cos 2x = 2 cos2 X-1

Q: sin 0(3sin? 0+ 4cos? 0) = 3 cos 0 + cos³ 0 4. Prove that tan 0

A:

Q: 3) [~x cos² (x3/2 - 8) dx , A)sin (x/2 - 8) + C 1 = x3/2 – 8 3) 1 B) a32 - 8) + sin 2432 - 8) • C D)…

A:

Q: 8(cos² z – 1) sin z cos z – sin z

A: Given,           8cos2x-1sinxcosx-sinx

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A: since you have asked multiple questions in single request so we will be answering only first…

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A: Given: sinθ−cosθ2−1=−2sinθcosθ We have to prove the given identity. Identity used: sin2θ+cos2θ=1

Q: cos (4-360°)sin(-4) 5.2.1 tan A.cos 180° sin 10°.cos 120e 5.2.2 cos 80°,sin 150° 5.2.3 sin (540°-x)…

A: Since you have posted many questions here, I can answer only one at a time. Please repost other…

Q: tanº(x) cos“(x) O sin'(x)sec°(x)[7sin?(x) + 9cos²(x)] + C 63 tanʼ(x) [7tan²(x) + 9]+c 36

A: The properties to be used for solving the integral are: a) 1/cos4(x)=sec4(x) b) d(tanx)dx=sec2x c)…

Q: 1+sin A cos 2 sec u – cos µ = sin µ tan µ 4. + 2 sec 1 %3D cos A 1+sin A

A: We have to verify the given identities.

Q: 5(cos²æ – 1) sin x cos x sin x - ||

A: Using trigonometric formula, given trigonometric function is simplified.

Q: sin 2 2) = (9z + 4), h(3) (2) (1) = sin(cos r), f"(1) %3D

A: