sin x) dr Evaluate: sin(x) + 1 1- sin(x) A +x+C cosx 1+ sin(x) B cos(x) x+C (c) cos(x) +C cos(x) - x 2cos(x) +C 1+ sin(x) D

Q: cos( - x) = O sin( - x) O cos( + x) cos( - x) sin( + x)

A: The given expression is: cos π3-x Note that: cos θ=sin π2-θ

Q: x´ tanh x f (x)= tan -1 (x)%3Dtan 2 sin x+ coS X

A: This is a problem of Differential Calculus.

Q: 2 (sin -'x)²dx Evaluate the integral [(sin -'x) dx V1-x

A:

Q: cos (x sin )=√₁ (x)+2 J₂ (x) cos 26+2 J₁ (x) cos 44+... sin (x sin )=2 J₁ (x) sin +2 J, (x) sin 36 3…

A: Using generating function of Bessel functions

Q: Verify the identity:

A: The given identity is sin3x+cos3x=sinx+cosx1-sin2x2

Q: csc(x) – 1 sec(x) Differentiate: f (x) = (A f'(x) = - csc²(x)+ sin(x) B B f'(x) = - csc2(x) – cos(x)…

A: We can use differentiation of trigonometric function rules to find the derivative of the given…

Q: sin x+cosX Differentiate y = %3D sin x-cos x 2 А. 1-sin 2x -2 В. 1+sin 2x -2 С. 1-sin 2x 2 D. 1+sin…

A: Given,  y=(sinx+cosx)/(sinx-cosx)

Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: 3(cos a- 1) sin x cos – sin x O 3 cotx+3 csc x O 3 tanx+3 csc x O 3 tan x +3 sec x O 3 cot x +3 sec…

A: Here we have to find the value of    3(cos2x -1)/(sin x cos x - sin x)

Q: sin(x)=−0.2cos(y)=0.4tan(z)=5.5 sin(−x)= 0.2cos(−y)= 0.4tan(−z)= -5.5 What does…

A:

Q: Verify the identity.

A: Use the trigonometric identities sinA+sinB=2sinA+B2cosA-B2 and cosA+cosB=2cosA+B2cosA-B2 to simplify…

Q: 1/sin(x)/cos (x)+cos (x)/1+sin(x)=4 Prove

A: For x= pi/3

Q: sin x(cos x-1) 8. Prove sin(n -x) – tan(t + x) | COSX

A:

Q: sin 2x+cos2x+1 1- Prove cot x sin 2x-cos 2x+1 2- Sinh (u-v) = Sinh u.Cosh v - Cosh u.Sinh v %3D

A: Evaluate the following 1-prove sin 2x+cos 2x+1/sin 2x-cos 2x+1=cot x 2-sinh(u-v) = sinh u.cosh v-…

Q: sin 5x + sin 3x 2 cOS X 4 sin x cos 4 sin x cos x 3 X COS -

A:

Q: Use identities to simplify each expression.

A: cosxsin2x+cos3xsecx=cosxsin2xsecx+cos3xsecx=cos2xsin2x+cos4x…

Q: sin x - cos x = 1/5, what is (sin x) (cos x) equivalent to?

A:

Q: sin (3x) + cos (3x) cos(x) – =1+4sin(x)cos(x)

A: We use sin(3x)= 3sinx-4sin3x and cos (3x)= 4cos3x-3cosx .

Q: sin x- cos x sin xcosx- cos x .2 CoS

A: To simplify

Q: sin 2 x + sin x + cos 2 x - 1 = _______ tan x cot x sin x cos x

A: We can solve it as below.

Q: sin(cosx * x + Vx) (cosx)2 sin (x²) * cos(x –-) sin(x) – 2

A:

Q: S(csc x cot x + 7x°)dx O sin x – x' + c O cos x + x7 +c .7 O cot x + x' + c tan x + x' +c - csc x +…

A: To integrate.

Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

A:

Q: sin x COsx Prove 2tanx secx - - cosx 1+ sin x

A: We use the identity sin2x + cos2x=1

Q: sin x cos x – tan x cos² x dx cos x cos? x sin x dx cos3 x 16. = sec x dx + cos x Let u = cos x ; du…

A: It is given that    ∫cosx-tanxcos2x dx We have to evaluate it.

Q: tan6(x) cos4(x) sin²(x)sec³(x) [7sin²(x) + 9cos²(x)] + C A 63 tan²(x) [7tan²(x) +9] + C B 36 Ⓒ…

A:

Q: 14) f' (x) =(sin 3 x)'=, A) – 3(cot2 x) csc2x C) 3(tan2 x) sec2x By Power Rule B) – 3 sin2 x cos x…

A:

Q: f-\(x) = sin='(x) а. 2'2 f-l(x) = cos-'(x) (-) b. 2' 2 f-|(x) = tan¬'(x) c. [0, n] f-(x) = cot"(x)…

A: This is a problem of fundamentals of trigonometric identities. Please find the solution below.

Q: Prove that

A: Given:d2ndx2nsinx=-1n sinxd2ndx2ncosx=-1n cosx

Q: Verify the following identity:

A: We have to prove the following trigonometric identity: sin4x2-cos4x2sin4x2cos4x2=-16cos xsin4 x

Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

A:

Q: V1+ cos x + v1- cos x X =-+-,0<x<. 4 2 an 1+ cos x - V1- cos x - cOS X VI

A:

Q: tan(x) dx cos4(x) tan'(x) A [7tan²(x) +9] + C 36 1 ℗tan'(x) + tan³(x) + C C D sin²(x)sec³(x)…

A:

Q: sin 2x + sin x + cos 2x - 1 = _______ cos x cot x tan x sin x

A: Solution ) sin2x + sin x + cos2 x - 1  = sin2 x + cos2 x + sin x - 1 We know that  [ sin2 x + cos2 x…

Q: . sin 2x cos x+ cos 2 sin x = 12

A:

Q: sin 3x-sin x Prove tan x. cos 3x+cos x

A:

Q: cos(x+π6)+sin(x−π3)=______

A:

Q: cos(x (*). cos(x + h) – cos x cos h – 1 sin h - - sin x · h COS x h h

A: Require to verify the identity cosx+h-cosxh=cosxcosh-1h-sinxsinhh

Q: lim sin(2 cos(z) Cos(z) 2

A: Limit problem....

Q: sin^2 x + sin x cos x over cos x − 2 cos^3 x

A: This question is based on Trigonometric Formulas to simplify question.

Q: sin x – cos r cos z cos 2x sin x + cos x 1+ sin 2x

A: Given, sinx-cosxsinx+cosx We need to prove that the value of sinx-cosxsinx+cosx is -cos2x1+sin2x…

Q: sin'x cos'xdk 3. X COS

A: It is given that, ∫sin2xcos3x dx We have to solve it.

Q: / Vtan(x) d.x sin(2r) I Vtan(x) -dx sin(2x) -d.x sin x cos x /cos x 2 Multiply by something that is…

A: We have to find integration

Q: cOs x sin x tan x (7) = sin x+ cos x 1- tan x tan x-1

A:

Q: cos 2x 25. cos x- sin x A sinx cos X cos x + sin x 2 cos x + sin x cos x - 2 sinx B 2 sin

A:

Q: sin x cos x 1 1. - sin – sin x 2 sinx cosx 3 cosx -1

A: The solution is given as

Q: sin-1 x = cos s-'(1 – 2x²) x > 0. |

A: The above problem is solved.

Q: sin x 25) lim x→0 5x 3(1 – cos x) 26) lim sin x (1 – cos x) 27) lim 2x2

A:

Q: 1-tan x 1+ tan x sec x-CsC X a. sin x + cos x sin x COS X b. sin x +cosX sin x + cos X C. sin x- cos…

A: