MCQ
$\sqrt{\frac{1-\sin \theta}{1+\sin \theta}}= ?$
- A$\sec \theta+\tan \theta$
- ✓$\sec \theta-\tan \theta$
- C$\operatorname{cosec} \theta+\cot \theta$
- D$\operatorname{cosec} \theta-\cot \theta$
✓
Answer
Correct option: B.
$\sec \theta-\tan \theta$
$ \sqrt{\frac{1-\sin \theta}{1+\sin \theta}}$
$\sqrt{\frac{1-\sin \theta}{1+\sin \theta}} \times \sqrt{\frac{1-\sin \theta}{1-\sin \theta}}$
$= \frac{1-\sin \theta}{\sqrt{1-\sin ^2 \theta}}$
$= \frac{1-\sin \theta}{\cos \theta}=\frac{1}{\cos \theta}-\frac{\sin \theta}{\cos \theta}$
$= \sec \theta-\tan \theta$
$\sqrt{\frac{1-\sin \theta}{1+\sin \theta}} \times \sqrt{\frac{1-\sin \theta}{1-\sin \theta}}$
$= \frac{1-\sin \theta}{\sqrt{1-\sin ^2 \theta}}$
$= \frac{1-\sin \theta}{\cos \theta}=\frac{1}{\cos \theta}-\frac{\sin \theta}{\cos \theta}$
$= \sec \theta-\tan \theta$
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