1+ 1- is equal to: - Vidyadip

MCQ

$\sqrt{\frac{1+\sin\theta}{1-\sin\theta}}$ is equal to:

✓
$\sec\theta+\tan\theta$
B
$\sec\theta-\tan\theta$
C
$\sec^2\theta+\tan^2\theta$
D
$\sec^2\theta-\tan^2\theta$

✓

Answer

Correct option: A.

$\sec\theta+\tan\theta$

$\sqrt{\frac{1+\sin\theta}{1-\sin\theta}}=\sqrt{\frac{(1+\sin\theta)(1+\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}}$
$=\sqrt{\frac{(1+\sin\theta)^2}{1-\sin^2\theta}}$
$=\sqrt{\frac{(1+\sin\theta)^2}{\cos^2\theta}}=\frac{1+\sin\theta}{\cos\theta}=\frac{1}{\cos\theta}+\frac{\sin\theta}{\cos\theta}$
$=\sec\theta+\tan\theta$

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