Question

Prove that ( Class 10 trigonometry ) ​​

Answer 1

Step-by-step explanation:

We have,

$\frac{ \tan^{2} ( \theta) }{1 + \tan^{2} ( \theta) } + \frac{ \cot^{2} ( \theta) }{1 + \cot^{2} ( \theta) }$

$= \frac{ \tan^{2} ( \theta) }{1 + \tan^{2} ( \theta) } + \frac{ \frac{1}{\tan^{2} ( \theta) }}{1 + \frac{1}{\tan^{2} ( \theta) }}$

$= \frac{ \tan^{2} ( \theta) }{1 + \tan^{2} ( \theta) } + \frac{ 1}{1 + \tan^{2} ( \theta) }$

$= \frac{ 1 + \tan^{2} ( \theta) }{1 + \tan^{2} ( \theta) }$

$= 1$