Question

Rewrite with only sin x and cos x.
sin 3x - cos x

Answer 1

sin 3x - cos x = 3 (sin x)(cos x)(cos x) -(sin x)(sin x)(sin x) -cos x

Explanation:

sin 3x - cos x

This uses Trig Identities.

sin 3x = sin (x + x + x) = sin (x+x)*cos x + cos (x + x) sin x

= 2sinxcosx * cos x + [ (cos x)(cos x) -(sin x)(sin x) ] (sin x)

sin 3x - cos x = 2sinxcosx * cos x + [ (cos x)(cos x) -(sin x)(sin x) ] (sin x) -cos x

sin 3x - cos x = 2sinxcosx * cos x + sinx (cos x)(cos x) -(sin x)(sin x)(sin x) -cos x

sin 3x - cos x = 3 sinx cosx * cos x -(sin x)(sin x)(sin x) -cos x

sin 3x - cos x = 3 (sin x)(cos x)(cos x) -(sin x)(sin x)(sin x) -cos x