Question

If ${\cot }^2\theta -\frac{1}{{\sin }^2\theta }=m$.Find $-m$

Answer 1

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

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

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

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

$=$ $-1$