Question

Prove that $(1-Si{n}^2\Theta )Se{c}^2\Theta =1$

Answer 1

$(1-{\sin }^2\theta )\left({\sec }^2\theta \right)=1$

$[{\sin }^2\theta +{\cos }^2\theta =1]$

$\therefore [1-{\sin }^2\theta ={\cos }^2\theta ]$

$[\sec \theta =\frac{1}{\cos \theta }]$

$\therefore L.H.S:(1-{\sin }^2\theta )\left({\sec }^2\theta \right)$

$={\cos }^2\theta \times \frac{1}{{\cos }^2\theta }$

$=1$

$=R.H.S$