Rewrite with only sin x and cos x.

sin 3x - cos x

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

Step-by-step 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