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

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