Question

How do you prove sin3x=3cos^2xsinx-sin^3x?

Answer 1

See below

Explanation:

`sin3x=3cos^2xsinx-sin^3x`

`sin(2x+x)=3cos^2xsinx-sin^3x`

Apply sine sum identity:
`sin2xcosx+cos2xsinx=3cos^2xsinx-sin^3x`

Apply sine and cosine double angle identities:
`(2sinxcosx)cosx+(cos^2x-sin^2x)sinx=3cos^2xsinx-sin^3x`

Simplify:
`2sinxcos^2x+cos^2xsinx-sin^3x=3cos^2xsinx-sin^3x`

`3cos^2xsinx-sin^3x=3cos^2xsinx-sin^3x quad sqrt`