Question

Make the following expression 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 ${\sin }^2\theta +{\cos }^2\theta =1$]

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

Which is perfect square.