Question

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

Answer 1

To prove:- ${(\cos \theta +\sin \theta )}^2+{(\cos \theta -\sin \theta )}^2=2$

Proof:-

Taking L.H.S.-

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

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

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

$=2$

$=$ R.H.S.

Hence proved.