how 2sinthetacostheta=sin2thetaexplain the above question

You may solve the problem either transforming the
product`sin theta*cos theta`  into a sum of two like trigonometric function or writing
the double of the angle `theta`  as the sum `theta + theta`
.

I'll focus on the first solving strategy such
that:

`sin theta*cos theta = (1/2)[sin(theta - theta) + sin
(theta + theta)]`

`sin theta*cos theta = (1/2)[sin(0) + sin
(2theta)]`

Since sin 0 = 0 => `2sin theta*cos theta
= sin (2theta)`

This last line proves the
given identity.