Question

please answer this question ​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Here,3 properties are used :

1.$\bold{\boxed{ {sin}^{2} \theta + {cos}^{2} \theta = 1}}$

2.$\bold{\boxed{1 + {tan}^{2} \theta = {sec}^{2} \theta}}$

3.$\bold{\boxed{1 + {cot}^{2} \theta = {cosec}^{2} \theta}}$

Come to the question:

Taking L.H.S =>

$= > \dfrac{1}{(1 +{tan}^{2} \theta)} + \dfrac{1}{(1 +{cot}^{2} \theta)}$

By using 2 and 3 property :-

$= > \dfrac{1}{ {sec}^{2} \theta } + \dfrac{1}{{cosec}^{2} \theta}$

We know that sec is the inverse of cos and cosec is the inverse of sin:

$\bold{= > {cos}^{2} \theta + {sin}^{2} \theta = 1}$(by using property 1)

Hence ,proved