Question

Find the value of ${(\sin \theta +\cos \theta )}^2+{(\sin \theta -\cos \theta )}^2$

Answer 1

We have${(\sin \theta +\cos \theta )}^2+{(\sin \theta -\cos \theta )}^2$
$={\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta +{\sin }^2\theta +{\cos }^2\theta -2\sin \theta \cos \theta$
$=2[{\sin }^2\theta +{\cos }^2\theta ]=2\left(1\right)=2$ $(\because {\sin }^2\theta +{\cos }^2\theta =1)$