Question

Make the following expression a perfect square:

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

Answer 1

Now,

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

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

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

This is the required perfect square term.