Question

Prove that following trigonometric identities :
${\cot }^2\theta -\frac{1}{{\sin }^2\theta }=-1$

Answer 1

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

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

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