Question
Write ‘True’ or ‘False’ and justify your answer.
$\sqrt{(1-\cos^2\theta)\sec^2\theta}=\tan\theta$
$\sqrt{(1-\cos^2\theta)\sec^2\theta}=\tan\theta$
✓
Answer
True.LHS $=\sqrt{(1-\cos^2\theta)\sec^2\theta}=\sqrt{\sin^2\theta.\frac{1}{\cos^2\theta}}$
$=\sqrt{\frac{\sin^2\theta}{\cos^2\theta}}=\tan\theta=$ RHS
Hence, the given expression is true.
$=\sqrt{\frac{\sin^2\theta}{\cos^2\theta}}=\tan\theta=$ RHS
Hence, the given expression is true.
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