Question #7cfc8

1 Answer
Oct 5, 2016

Proof below

Explanation:

First we will find the expansion of sin(3x) separately (this will use the expansion of trig functions formulae):
sin(3x)=sin(2x+x)
=sin2xcosx+cos2xsinx
=2sinxcosxcosx+(cos2xsin2x)sinx
=2sinxcos2x+sinxcos2xsin3x
=3sinxcos2xsin3x
=3sinx(1sin2x)sin3x
=3sinx3sin3xsin3x
=3sinx4sin3x

Now to solve the original question:
sin3xsinx=3sinx4sin3xsinx
=34sin2x
=34(1cos2x)
=34+4cos2x
=4cos2x1
=4cos2x2+1
=2(2cos2x1)+1
=2(cos2x)+1