How do you prove #Sin(x/3)cos(x/3) = (1/2)sin(2x/3)#?

1 Answer
Apr 27, 2018

We substitute #theta=x/3# in the #sin(2 theta ) = 2 sin theta cos theta#
and we're home.

Explanation:

The double angle formula for sine is

#sin(2 theta ) = 2 sin theta cos theta#

That's an old saw your teacher will generally accept without proof.

Setting #theta = x/3#,

#sin(2 cdot x/3) = 2 sin (x/3) cos(x/3) #

# 1 /2 sin((2x}/3) = sin (x/3) cos(x/3) quad sqrt#