Question

Prove the identity with all steps
Cos3x＝cos^3x-3sin^2xcosx

Answer 1

Try the identity cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
with A = 2x and B = x as a first step. Then expand cos(2x) and sin(2x).

Answer 2

cos(3x) = cos(2x + x) = cos(2x)cos(x) - sin(2x)sin(x) =
{ cos^2(x) - sin^2(x) }*cos(x) - 2sin(x)cos(x)sin(x) =
cos^3(x) - sin^2(x)cos(x) - 2sin^2(x)cos(x) =
cos^3(x) - 3sin^2(x)cos(x)

Answer 3

Thank you I was hitting a wall with this problem

Answer 4

You are welcome.