Could you please help me verify the expression 4cos^3 (x) - 3cos(x) = cos^3 (x) - 3sin^2 (x) cos(x)

Answer 1

cos x (cos²x-3sin²x) Factor out a cos x

cos x (cos²x-3(1-cos²x)) Substitute 1-cos²x for sin²x, this is a Pythagorean identity.

cos x (cos²x-3+3cos²x)) Distribute the -3

cos x (4cos²x-3) Combine like terms

4cos³x-3cos x Distribute the cos x, now they match