Question

Prove that : $\frac{({\sin }^4\theta +{\cos }^4\theta )}{1-2{\sin }^2\theta {\cos }^2\theta }=1$

Answer 1

L.H.S

$\begin{array}{c}\frac{{\sin }^4\theta +{\cos }^4\theta }{1-2{\sin }^2\theta {\cos }^2\theta }\\ =\frac{{\left({\sin }^2\theta +{\cos }^2\theta \right)}^2-2{\sin }^2\theta {\cos }^2\theta }{1-2{\sin }^2\theta {\cos }^2\theta }\\ =\frac{1-2{\sin }^2\theta {\cos }^2\theta }{1-2{\sin }^2\theta {\cos }^2\theta }=1\end{array}$

Hence, proved.