Question

Prove that :
$co{s}^2\theta (1+ta{n}^2\theta )=1.$

Answer 1

We have,

LHS = $co{s}^2\theta (1+ta{n}^2\theta )$

$\Rightarrow LHS=co{s}^2\theta se{c}^2\theta$ $[\because 1+ta{n}^2\theta =se{c}^2\theta ]$

$\Rightarrow LHS=co{s}^2\theta \left(\frac{1}{co{s}^2\theta }\right)$ $[\because sec\theta =\frac{1}{cos\theta }]$

$\Rightarrow$ LHS = 1 = RHS