• tan°(x) Xp- cos“(x) 1 1 tan9

Q: Part A (i) Let f(x) = ln(3ª + 8"). Find f'(x). %3D (ii) Find 2" cos(r)` cos(2") d da

A: Derivative of function

Q: The function y sin a is also which of the following functions?

A:

Q: sin (t) -dt 3 (4+ cos (t))?

A:

Q: Match the function with the graph (1) y = -1 + cos x

A:

Q: S cos (oc) Sin (x) + 3√ sin(x) dx

A: We need to evaluate :

Q: y + (cos x) y =3 sinx.cosx

A:

Q: • 7/40 8000 sin (20x) Evaluate dx 7/60 1 – 2 cos (20x)

A: To evaluate: ∫π60π408000sin(20x)1-2cos(20x)dx...(1)

Q: 4x? )(i) Use the substitution x= tan e to show that sin? 20 dx. %3D (1+x*)' 4x2 (ii) Hence find in…

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Q: f(x) = (8 sin x + 3 cos x)tan1 -

A:

Q: cos( – x) + tan( – x)sin( – 2)

A:

Q: sec(t) – cos(t) - Simplify to a single trig function. sin(t)

A: Using trigonometric formulas

Q: S(sinx – cosx)²dx COoSx

A: Given, ∫sinx-cosx2dx  We have to find the integral.

Q: cos (E) U4+ tan(t)

A:

Q: 5cos³(x) sin(3–2x) answer in terms of sin and cos only ind the derivative of y = + tan²(3x² – 4x) –…

A:

Q: |(sin 3x + cos 2.x)* dx

A: Given integral is ∫sin3x+cos2x2dx

Q: R/2 7 cos?(0) do

A:

Q: cos x csc3 x + C sin4 x 1.

A: To evaluate the given integral.

Q: (cos x)(sin x)V1 – sin x dx

A: Let sin x = t , hence, cos x dx=dt . The integral, ∫(cos x)(sin x)1-sin xdx can be written as ∫(sin…

Q: sin(cos (2x)), where 0<x<

A:

Q: |(sin 3x + cos 2x) dx

A: Definition used -                                (a+b)2=a2+2ab+b2…

Q: 4 sin x dx (1 + cos x)²

A: Here we have to solve the given integration.

Q: T/3 sin x dx COsx -1

A: I have stated the used formulas in the solution.

Q: (g) sin 3

A: To find the value of

Q: π/4 IF ST/A tan (x) sec(x) dx = I, express the value of 。 π/4 tan (x) sec(x) dx in terms of I.

A: Given:- ∫0π4tan4xsecxdx=I

Q: 1. f cos³ (tan x) sec² x dx

A:

Q: sin x dx 2- cos²x CoS

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Q: ( (cos(2r) – sin(2x)cos(2x)) -dx =. For +C. What is F (x)? cos(x) – sin(x)

A:

Q: 8 csc? 4x cos(cot(4x)) dx sin² (cot(4x))

A: Here, I will be using method of substitution to solve this integral. You can assume:…