Question

Prove the following trigonometric identities:

$\frac{(1+co{t}^2\theta )tan\theta }{se{c}^2\theta }=cot\theta$

Answer 1

Taking LHS we have

$\frac{(1+co{t}^2\theta )tan\theta }{se{c}^2\theta }$
[Here, 1 + $co{t}^2\theta =cose{c}^2\theta$]
$\frac{cose{c}^2\theta tan\theta }{se{c}^2\theta }$

$\to$ $\frac{1}{Si{n}^2\theta }$ . $\frac{1}{Se{c}^2\theta }$ . $\frac{Sin\theta }{Cos\theta }$

$\to$ $\frac{1}{Si{n}^2\theta }$ . $Cos\theta$ $Cos\theta$ $\frac{Sin\theta }{Cos\theta }$
$\to$ $\frac{Cos\theta }{Sin\theta }$
$\to$$Cot\theta$ = RHS

Hence proved.