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

1 Answer
Apr 28, 2018

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#