Question

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

Answer 1

LHS$=\frac{1}{{\sin }^2\theta }-\frac{1-{\sin }^2\theta }{1-{\cos }^2\theta }$
$=\frac{1}{{\sin }^2\theta }-\frac{{\cos }^2\theta }{{\sin }^2\theta }(\because {\sin }^2\theta +{\cos }^2\theta =1)$
$=\frac{1-{\cos }^2\theta }{{\sin }^2\theta }=\frac{{\sin }^2\theta }{{\sin }^2\theta }=1$