Verify the identity. sin (e + n) = -sin e A) sin (e+x) = cos Osin e- cosa sin a = cos Osin e--0 = -sin e C) in (8+x) = cos Ocos a - sin Osin a = cos 8.-1- sin e -0 =-sin e B) sin(e +x) = sin Ocos e + cosa sin a = sin Ocos e + sin a = -sin e D) sin(@ +x) = in OcosA + cos Osina = in -1+cos e -0 = -sin e %3D %3D %3D

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

Q: If e 2i =sin2 then z = = sin2 = 2 - 2 In(sin2) + 4kT 2i In(sin2) + 4k TI - 2i In(sin2) – 4k T | - 2i…

A: Given that, e-z2i=sin2e-z2i=sin 2e-z2i×ii=sin 2eiz2=sin 2

Q: Verify the identity. csc(x) cos²(x) + sin(x) = = = csc(x) cos²(x) + sin(x) = csc(x) 1 sin(x) 1 2…

A: Given csc(x)cos2(x)+sin(x)=csc(x)

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

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

A:

Q: Verify the identity: sin(x - y)/(cos x cos y) + sin(y - z)/(cos y cos z) + sin(z - x)/ (cos z cos x…

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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: Setting x= cos or cosho show that Tn(x)==[(x + √X²_₁ )² + (x-√x ²₁ ²]

A:

Q: Evaluate sin (; - i In v2) cos(; - i In i ln v2) i In /2) cos o (3/4)i o (3/8)i o 5/8 o 5/4

A:

Q: Establish the identity. sin x- sin y x+y cot 2 COS X- COs y Which of the choices shows the key steps…

A: To prove the following trignometric identity:

Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

A: Explanation of the solution is given below.....

Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

A:

Q: sin 2x, Which of the following is equal to sin x cOs x + C 2 sin x + C Option 1 Option 2 sin 2x + C…

A: As we know that the trigonometric identity: sin2x=2sinxcosx And ∫a·fxdx=a∫fxdx Given: I=∫sin2xsinxdx

Q: Prove the identity: cos(x + y)cos(x – y) = cos?x – sin²y

A:

Q: Prove the identity cos(x+y)cos y +sin(x+ y)siny =cos x

A: We have to prove the identity                              cosx+ycosy+sinx+ysiny=cosx

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: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

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Q: Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x…

A:

Q: sin e 1 cos 0 Multiply - by 1 + cos 0 1 - cos 0

A: According to the difference of squares formula, (a+b)(a-b)=a2-b2. Using the difference of squares…

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: sin(1) dt Using an appropriate substitution, evaluate: [2+ cos(t)]* A +C 3[2+ cos(t)]3 3 B +C [2+…

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: 2) cos (0 + n) = -cos e =-COS

A:

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: Verify the identity. cos(e) sin(0) - csc(0) 1- sin(0) cos(0) - cot(0) sin(e) – sin(0) sin(e) –…

A:

Q: Verify the identity. 1 + sin 2x cos x+ sin x %3D cos 2x cos x- sin x Choose the sequence of steps…

A: Sin2x correct formula is- Sin2x=2SinxCosx So this formula is only used in option 2

Q: cos 2r Verify the identity: = cos x + sin x. sin x cos X

A: Verify the following: cos 2xcos x-sin x=cos x+sin x

Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: Prove that sin? 0 – sin* 0 = cos? 0 – cos* 0. cos“ 0.

A: We can use the trigonometric identity, sin2θ+cos2θ=1 sin2θ=1-cos2θ.

Q: Verify the identity. (1 - sin (t) + 6 cos (t))2 + 49 sin2(t) cos2(t) = 49 cos (t) %3D (1 - sin?(t) +…

A: we know   ,                Sin2( t )+ cos2(t) = 1    implie ,  1 -  Sin2(t) =  cos2(t)

Q: Prove that sin? 0 + cosª 0 = sin“ 0 + cos² 0.

A: Using fundamental identity of trigonometry.

Q: Verify the identity (1+sin x)(1-sin x)=cos2x   (sin x + cos x)2 + (sin x - cos x)2=2   cot(x) =…

A: (1+sin x)(1-sin x)=cos2x Apply FOIL method to expand left side

Q: (a-B) (at sin (a+B) 2- show that cosa – cosß = -2sin 2.

A:

Q: - Prove that tan 0 + cos 0 sin 0 cos 0 cos 0T sin 0 - Prove that cos? 0 – sin² 0 cos? 0 + sin A cos…

A:

Q: cos e sin 0 for some real value of 0, and let B= -1 Let A = Consider x - sin 0 cos 0 Then ||(AB)x||…

A: Given,            A=cosθsinθ-sinθcosθ , B=0-1-10 , x=12To find : ABx

Q: Verify the identity. sin³(x) + cos³(x) = 1 – sin(x) cos(x) sin(x) + cos(x) sin3(x) + cos³(x) sin(x)…

A: we know that  a3+b3=a+ba2-ab+b2

Q: Verify the identity. 1 - cos(a) sin(a) sin(a) 1 + cos(a) 1- cos(a) 1- cos(a) . 1 + cos(a) 1 + cos(a)…

A:

Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?   −2   1   2   −1

A: We have to find

Q: tan(x) – cos²(x) dx Evaluate: cos(x) A sec(x) -sin (х) +с B B sec(x) + sin(x) + C © sin(x) – sec(x)…

A: We can find the integration as below

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)…

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Q: Verify the identity. 5 cos(sin x) = V 25 25x2 %3D Let 0 = sin 1x → sin 0 = x = 4. -수 Thus, %3D %3D 5…

A:

Q: Solve for θ : (cos θ + i sin θ) (cos 2θ + i sin 2θ) …. (cos nθ + i sin nθ) = i

A: We have to solve for θ: (cos θ + i sin θ) (cos 2θ + i sin 2θ) …. (cos nθ + i sin nθ) = i Then we…

Q: Establish the identity. sin 0+ sin (30) cos 8- cos (30) Choose the correct sequence of steps to…

A:

Q: Verify the identity: [cos(x + h) - cos x]/h = cos x. (cos h - 1)/h - sin x. (sin h)/h

A: we have to verify the identity : cos(x+h)-cosxh=cosx(cosh-1)h-sinx(sinh)h

Q: sin 5x sin adx =? O A, sin 4x sin 6x +c 6 4 sin 4x sin 6x OB. 8. +c 12 O C cos 4x 8 cos 6z +c 12 O D…

A:

Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

A:

Q: de 2- sin(e) ( cos(e) de 1+cos(0) de 2- 3sin(e) de 3sin(e) + 4cos(e) + 5 de sin(e) + 3cos(6) + 3

A: SOLUTION Given ∫dθ2 -sinθ∫cosθ dθ1+cosθ∫dθ2-3sinθ∫d θ3 sinθ+4 cosθ+5∫d θsinθ +3 cosθ+3 we need to…

Q: now that cos(ak – a/2) 2 sin(a/2) E sin(ak) : (1 %3D Taking the difference of cos(ak), A cos(ak) =…

A: We have to solve given problem:

Q: Verify the identity. 1+ sin(x) = (tan(x) + sec(x))² 1+ sin(x) 1 - sin(x) 1- sin(x) 1+ sin(x). 1 +…

A: