Question

${(1+\sin \theta +\cos \theta )}^2=2(1+\sin \theta )(1+\cos \theta )$

• A. True
• B. False

Answer 1

The correct option is A True

$(1+\sin \theta +\cos \theta {)}^2=1+{\sin }^2\theta +{\cos }^2\theta +2\sin \theta +2\cos \theta +2\sin \theta \cos \theta$

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

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

$=2(1+\sin \theta +\cos \theta +\sin \theta \cos \theta )$

$=2(1+\sin \theta )(1+\cos \theta )$

So the given relation is $\text{True}$