how 2sinthetacostheta=sin2thetaexplain the above question

You may solve the problem either transforming the
product  into a sum of two like trigonometric function or writing
the double of the angle   as the sum
.

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

(theta + theta)]

(2theta)]

Since sin 0 = 0 =>
= sin (2theta)

This last line proves the
given identity.