Prove the following identites: (1- ^2 ) ^2 = ^2 - Vidyadip

Question

Prove the following identites:
$\big(1-\cos^2\theta\big)\sec^2\theta=\tan^2\theta$

✓

Answer

$\text{L.H.S.}=\big(1-\cos^2\theta\big)\sec^2\theta$
$=\sin^2\theta\times\sec^2\theta$ $\begin{bmatrix}\because\big(1-\cos^2\theta\big)=\sin^2\theta\end{bmatrix}$
$=\sin^2\theta\times\frac{1}{\cos^2\theta}=\frac{\sin^2\theta}{\cos^2\theta}$
$=\tan^2\theta$
$=\text{R.H.S.}$
$\therefore\ \text{LHS}=\text{RHS}$

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