Question

Evaluate
${\cos }^4\theta +{\sin }^4\theta =1-2{\cos }^2\theta .{\sin }^2\theta$

Answer 1

$R.H.S=1-2{\cos }^2\theta .{\sin }^2\theta$

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

$={\sin }^4\theta +{\cos }^4\theta +2{\cos }^2\theta .{\sin }^2\theta -2{\cos }^2\theta .{\sin }^2\theta$

$={\sin }^4\theta +{\cos }^4\theta$

Hence proved