Question

Prove that :
$co{s}^2\theta +\frac{1}{1+co{t}^2\theta }=1$

Answer 1

We have,
$LHS=co{s}^2\theta +\frac{1}{1+co{t}^2\theta }$

$\Rightarrow LHS=co{s}^2\theta +\frac{1}{cose{c}^2\theta }$....................... $[\because 1+co{t}^2\theta =cose{c}^2\theta ]$

$\Rightarrow LHS=co{s}^2\theta +si{n}^2\theta =1$ ......................$[\because \frac{1}{cosec\theta }=sin\theta ]$

$\Rightarrow$ LHS = $1$ = RHS.