Question
Prove the following identity:
$
\left(1-\sin ^2 \theta\right) \sec ^2 \theta=1
$
$
\left(1-\sin ^2 \theta\right) \sec ^2 \theta=1
$
✓
Answer
$
\begin{aligned}
& \left(1-\sin ^2 \theta\right) \sec ^2 \theta=1 \\
& \text { Consider L.H.S }=\cos ^2 \theta \sec ^2 \theta \\
& =\cos ^2 \theta \times \frac{1}{\cos ^2 \theta}=1 \\
& =\text { R.H.S }
\end{aligned}
$
Hence proved.
\begin{aligned}
& \left(1-\sin ^2 \theta\right) \sec ^2 \theta=1 \\
& \text { Consider L.H.S }=\cos ^2 \theta \sec ^2 \theta \\
& =\cos ^2 \theta \times \frac{1}{\cos ^2 \theta}=1 \\
& =\text { R.H.S }
\end{aligned}
$
Hence proved.
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