Question

Prove the above result​

Answer 1

Step-by-step explanation:

We know that

$1 + \cot {}^{2} (x) = \csc {}^{2} (x)$

$or \: 1 + \cot {}^{2} ( - x) = \csc {}^{2} ( - x)$

Multiplying both side by 2

$or \: 2 + 2 \cot {}^{2} ( - x) = 2 \csc {}^{2} ( - x)$

$or \: 2 + \cot {}^{2} ( - x) = 2 \csc {}^{2} ( - x) - \cot {}^{2} ( - x)$

Taking reciprocal, we get

$\frac{1}{\: 2 + \cot {}^{2} ( - x)} = \frac{1}{ 2 \csc {}^{2} ( - x) - \cot {}^{2} ( - x) }$

Hence Proved.