Question : Solve the following equation.
$\sec ^2 \theta\left(\sqrt{1-\sin ^2 \theta}\right)= $ __________.
Option 1: $\tan \theta$
Option 2: $\operatorname{cosec \theta}$
Option 3: $\sec \theta$
Option 4: $1$
Correct Answer: $\sec \theta$
Solution :
The given equation is:
We know that $\cos^2 \theta = 1-\sin^2 \theta $.
$\sec ^2 \theta\left(\sqrt{1-\sin ^2 \theta}\right)$
$=\sec ^2 \theta\left(\sqrt{\cos^2 \theta}\right)$
$=\sec ^2 \theta\cos \theta$
$=\sec \theta $
Hence, the correct answer is $\sec \theta $.
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