1- 1+ =? - Vidyadip

MCQ

$\sqrt{\frac{1-\sin\text{A}}{1+\sin\text{A}}}=?$

A
$\sec\text{A}+\tan\text{A}$
✓
$\sec\text{A}-\tan\text{A}$
C
$\sec\text{A}\tan\text{A}$
D
None of these.

✓

Answer

Correct option: B.

$\sec\text{A}-\tan\text{A}$

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

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