Question

Please answer this question

Answer 1

hope u understand
IT IS VERY SIMPLE AND IN 5 STEPS U R DONE WITH UR ANSWER ........SIMPLE N BEST

Answer 2

We Have

$\huge \frac{1}{1 + \cos^{2} ( \alpha )} + \frac{1}{1 + \sin ^{2} ( \alpha ) } + \frac{1}{1 + \sec ^{2} ( \alpha ) } + \frac{1}{1 + \cosec ^{2} ( \alpha ) }$

We Know

$\sin( \alpha ) = \frac{1}{ \csc( \alpha ) }$

and

$\cos( \alpha ) = \frac{1}{ \sec( \alpha ) }$

Putting This In Question, We Get

$\huge \frac{1}{1 + \cos^{2} ( \alpha )} + \frac{1}{1 + \sin ^{2} ( \alpha ) } + \frac{1}{1 + \frac{1}{ \sin^{2} ( \alpha ) } } + \frac{1}{1 + \frac{1}{ \cos^{2} ( \alpha ) } }$

On Solving We Get,

$\huge \red {\frac{1 + sin^{2} \alpha }{1 + sin^{2} \alpha} + \frac{1 + cos^{2} \alpha }{1 + cos^{2} \alpha} }$

$\huge \blue {= 1 + 1}$

$\huge \orange {= 2 }$

Hence Proved :)