If x = b a , then a + b a - b + a - b a + b = - Vidyadip

MCQ

If $\tan x = \frac{b}{a},$ then $\sqrt {\frac{{a + b}}{{a - b}}} + \sqrt {\frac{{a - b}}{{a + b}}} = $

A
$\frac{{2\sin x}}{{\sqrt {\sin 2x} }}$
✓
$\frac{{2\cos x}}{{\sqrt {\cos 2x} }}$
C
$\frac{{2\cos x}}{{\sqrt {\sin 2x} }}$
D
$\frac{{2\sin x}}{{\sqrt {\cos 2x} }}$

✓

Answer

Correct option: B.

$\frac{{2\cos x}}{{\sqrt {\cos 2x} }}$

b
(b) Given that, $\tan x = \frac{b}{a}$

Now $\sqrt {\frac{{a + b}}{{a - b}}} + \sqrt {\frac{{a - b}}{{a + b}}}$

$= \sqrt {\frac{{1 + b/a}}{{1 - b/a}}} + \sqrt {\frac{{1 - b/a}}{{1 + b/a}}} $

$ = \frac{2}{{\sqrt {1 - \frac{{{b^2}}}{{{a^2}}}} }} = \frac{2}{{\sqrt {1 - {{\tan }^2}x} }} $

$= \frac{2}{{\sqrt {1 - \frac{{{{\sin }^2}x}}{{{{\cos }^2}x}}} }} $

$= \frac{{2\cos x}}{{\sqrt {\cos 2x} }}$.

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