Question

Prove that :
$ta{n}^2\theta -\frac{1}{co{s}^2\theta }=-1$

Answer 1

We have,

L.H.S. = $ta{n}^2\theta -\frac{1}{co{s}^2\theta }$

$\Rightarrow$ L.H.S. = $ta{n}^2\theta -se{c}^2\theta$ ..........................$[\because \frac{1}{cos\theta }=sec\theta \therefore \frac{1}{co{s}^2\theta }=se{c}^2\theta ]$

$\Rightarrow$ L.H.S. = $-(se{c}^2\theta -ta{n}^2\theta )=-1=R.H.S.$