I need help with verifying these trig identities:

Question

1) sin4x = 4sinxcos - 8sin^3 x cos x

2) cos3x = cos^3 x - 3sin^2 x cos x

Answer 1

sin4x = 4sinxcos - 8sin^3x cosx
sin4x = 4sinx*cosx(1-2sin^2x)
sin4x = 4sinx*cosx(cos2x)
sin4x = 2(2sinx*cosx)(cos2x)
sin4x = 2(sin2x)(cos2x)
sin4x = sin(2*2x)
sin4x = sin4x

cos3x
cos(x+2x)
cosx*cos2x - sinx*sin2x
cosx(1-2sin^2x) - sinx(2sinx*cosx)
cosx(1 - 2sin^2x - 2sin^2x)
cosx(1-4sin^2x)
cosx(cos^2x+sin^2x-4sin^2x)
cosx(cos^2x-3sin^2x)
cos^3x - 3sin^2x cosx