Question

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

Answer 1

${\sin }^4\theta +{\cos }^4\theta$
$=({\sin }^2\theta {)}^2+({\cos }^2\theta {)}^2$
$=({\sin }^2\theta +{\cos }^2\theta {)}^2-2{\sin }^2\theta {\cos }^2\theta$
$=1-2{\sin }^2\theta {\cos }^2\theta$
$=RHS$

$LHS=RHS$

hence proved