trig equation help?

Question

can i add ...for example...sin2x and sin3x
or does that not work?thx
its a summer assignment for calculus and im afraid i'm a bit rusty

Answer 1

Use the angle addition formulas for sine.

(sin 2x) + (sin 3x) = sin(x + x) + sin(2x + x)

= 2(sin x)(cos x) + (sin 2x)(cos x) + (cos 2x)(sin x)

= 2(sin x)(cos x) + (sin x)(cos x)(cos x) + (1 - 2sin²x)(sin x)

= 2(sin x)(cos x) + (sin x)(cos²x) + sin x - 2sin³x

= 2(sin x)(cos x) + (sin x)(1 - sin²x) + sin x - 2sin³x

= 2(sin x)(cos x) + sin x - sin³x + sin x - 2sin³x

= 2(sin x)(cos x) + 2sin x - 3sin³x

= 2(sin x)[cosx + 1] - 3sin³x

Answer 2

No. You can prove for yourself that this does not work by substituting real angles for x.