Question

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

Answer 1

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

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

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

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