Verify the identity. (Simplify at each step.) cos³ x sin³ x = (sin³ x sin x)cos x cos³ x sin³ x = (sin³ x) x) ( = = (sin³ x)(1 (sin³ x - sin5 x) cos x - cos COS X )cos x

Q: 4. sin 3x+cos 3x cos x-sin x = 1+ 4 sin x cos x

A:

Q: X 25 24 7

A:

Q: Express cos (a) in terms of cos(2a). Express sin (a) in terms of cos(2a). cos² (a) COS sin (a)

A: (a) We have to express cos2α in terms of cos2α.

Q: sin( – x) = cos x = COS X

A: Given: To prove that sin(π2-x)=cos x

Q: T (b) fo 6 sin 20 cos² 20 ӨР

A:

Q: 2. sin 2x 1 - sin² x = 2 tan x

A: Aim: To show that sin(2x)1-sin2(x)=2tan(x)

Q: Rewrite cos x + 3 in terms of sin(x) and cos(x). COS

A:

Q: Cos(11°+x)=-sin(2x+6)

A: x

Q: -5 sin x = -2 cos2 x + 4

A:

Q: 2x cos x? dx 1+ sin² x² 8

A:

Q: ·/₁ Evaluate cos x sin³ x dx. 2 cos(x) + cos¹ (x) ²/ X syntax error. + C

A: Given query is to find the integral.

Q: Im cos 2x + sin 2x} %3D Cos 4i - 4

A: To find: The imaginary part of -x4icos 2x+x4sin 2x. Concept used: If the complex number is written…

Q: 1. (cos5 2x sin5 2x) dx 2. (tan5 4x tan² 2x sec2x)dx 3. (sin 5x cos 5x)dx

A: Step 1:1. I=∫(cos5(2x)sin5(2x))dxLet v=2x. Then dv=2dx, so 21​dv=2dx.Rewrite using u1 and…

Q: (V1 + sin x cOS x dx

A:

Q: 3 cos xdx 1-sinx

A:

Q: rewrite cos(x+4pi/3) in terms of sin(x) and cos(x)

A:

Q: 1 - cos2 x/sin x

A: To simplify the expression.

Q: Making this substitution using [₁ gives us 10 sin²(x) cos³(x) dx 10 10 sin²(x) (1 - sin²(x)) cos(x)…

A: To evaluate the following integral. ∫10 sin2x cos3x dx Note: After seeing the previous solution, we…

Q: Write the expression cos (2 sin'x) as an algebraic expression in x, where (-1< x <1). Select one:…

A: