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

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

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Q: 1 cos(5x) +... 25 cos(x) + cos(3x) + Ans. + 2 sin(x)+ sin(3x) +sin(5x) +...

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Q: cos x sin* x dx 2. [ cor'x sin'x de 1. 7/4 7/3 3. cos x sin x dx 4. /4 | cos³x sin³ x dx

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: 2-sec2x: COS2X = COS X

A: Given query is to verify the identity

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: cos.2x 25. cos.x - sinx A sinx 3-.cos x + sinx C 2:cosx + sinx A - cos.x :D D cosx -2-sinx

A:

Q: sin(3x) cos(6x) – cos(3x) sin(6x) = -0.6 X =

A: There is trigonometric identity sinA-B= sinAcosB-cosAsinB

Q: b) (cosx+ Sinx)² - Cos x+sinx)(cosx-Sinac) tan 2x 2. c) 1-Cos-x - Sin2oc) Sin X - 2cos x

A:

Q: sin x cos 4x 32) lim X0 X+X cos 5x

A: Consider the given limit

Q: sin- In2 4+ tan-'cos- dx 2 2 I+ cos2* 4+ tan-'cos- In2 4+ tan-'cos- dx 2 2sin- 2 A 1+ cos 4+ tan…

A: To evaluate: ∫sin x2 ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: 2dx 2 2 cos x√ 4tanx - tan x S-

A:

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

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Q: 75. sin x cos x dx 76. sin 2x sin (cos 2x) dx

A: as per the company guidelines, I can solve only one question.

Q: sin( 2 cos (x/ 20 )) = Select one: O 2x (400 - x )°/(400 - 2x) O 40 x/ (400 + x) O ( 2x - 400 ) /…

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Q: cos x + sin² x + 1 dx cos² x (sin² x + 1)

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Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

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Q: 21. cos x cos 2x + sin x sin 2x

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Q: 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin¯' 5x)

A: some functions are given , we have to find its derivative

Q: cos 2x - 2 sin x- cosʻx=-3

A: Consider cos 2x-2 sin x-cos2 x=-3  . . . . . (1) We have cos 2x=2 cos2 x-1 . . . .  . . (2)

Q: 1. f(cos 3x - x²) (sin 3x- x³)5 dx 2. f cos² x (tan x) (sec² x − 1) dx 3. f tan x (sec² x - 1)(sec²…

A:

Q: sin (2x) dx 2. ( (sin(In x) + cos(In x)]² dx xp: 3x/10 In(3x) – (1In(3x))²

A:

Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

A:

Q: 8 sin x cos x sec x =

A:

Q: 11) cos x csc X tan x - 1 11) 12) cos2x - sin2x = 1 - 2 sin²x 12)

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Q: x2 sin x+2x cos x f'(x) = cos²x

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Q: lim (x approaches 0) of [sin(5x)cos(6x)]/(x)

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Q: 2 sin(x) cos(x) V3 cos(x

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Q: sin 2x cos x + cos 2x sin x = −1

A: sin(x+y)=sin(x).cos(y)+cos(x).sin(y) if sin (θ)=-1       then  θ=(2nπ+3π/2)  where n is an integer

Q: 1. sin x sin 2x + cos x cos 2x = COS X

A:

Q: 1. Integral of x sin^3 (x^2) 2. Integral of sin^4 3x

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Q: cos" x dx Cosn-1 x sin x n – 1 + п-2 Cos' x dx n n

A:

Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

A:

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: integral sin2 x cos3 x

A:

Q: cos^2x+sin^2x/cos^2x=

A:

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: 1+ cosx + sinx sinx 1+cos X 2sec x 2csc x 2csc 2x 2sec 2x

A:

Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

A:

Q: cos 2x cos.x+ sin x xp-

A:

Q: 1+sin x+cosx 1+cos x (b) 1+sinx-cos X sin x

A:

Q: Scos“ x- sin' xdx x•sin³ xdx 3

A:

Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…

Q: Solve over the interval [0,2pi)

A:

Q: 15. f(x)= sin 3x 17. f(x)= tan 2.x 19. f(x)= 3 cos (x – 7/2) -

A: 15) For sin(3x) the range of the function will  be the same as sin(x) just the period, in this case,…

Q: sin x cos x tan x = 1 – cos² x -

A:

Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x