Question

Write the value of ${\cot }^2\theta -\frac{1}{{\sin }^2\theta }$.

Answer 1

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

$={\cot }^2\theta -{\text{cosec}}^2\theta$

we know

$1+{\cot }^2\theta ={\text{cosec}}^2\theta \Rightarrow {\cot }^2\theta -{\text{cosec}}^2\theta =-1$

So,

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