Question

Make the following expression to be perfect square:

$1+\sin 2\theta$.

Answer 1

Given the expression is

$1+\sin 2\theta$

$=1+2\sin \theta .\cos \theta$

$={\sin }^2\theta +{\cos }^2\theta +2\sin \theta .\cos \theta$ [ Since ${\sin }^2\theta +{\cos }^2\theta =1$]

$=(\sin \theta +\cos \theta {)}^2$

This is the required perfect square expression.