Question

write the value of cot
square theta minus one upon sin square theta

Answer 1

I think this must be correct. You can further expand to find the correct ans.

Answer 2

Given:

The expression is

$\cot^2\theta - \dfrac{1}{\sin^2\theta}$

To find:

The value of given expression.

Solution:

We have,

$\cot^2\theta - \dfrac{1}{\sin^2\theta}$

$=\cot^2\theta - \text{cosec}\theta$      $[\because \dfrac{1}{\sin \theta}=\text{cosec}\theta]$

$=\cot^2\theta - (1+\cot^2\theta)$   $[\because \text{cosec}\theta=1+\cot \theta]$

$=\cot^2\theta - 1-\cot^2\theta$

$=-1$

Therefore, the value of $\cot^2\theta - \dfrac{1}{\sin^2\theta}$ is -1.