( x + x ) is equal to- - Vidyadip

MCQ

$\int {(\sqrt {\tan x} + \sqrt {\cot x} )} $ is equal to-

A
$sin^{-1} (sinx -cosx) + C$
✓
$\sqrt 2 \,sin^{-1} (sinx -cosx) + C$
C
$\sqrt 2 cos^{-1} (sinx -cosx) + C$
D
none of these

✓

Answer

Correct option: B.

$\sqrt 2 \,sin^{-1} (sinx -cosx) + C$

b
$\int \sqrt{\tan x}+\sqrt{\cot x} d x$

$\int \frac{(\sin x+\cos x) d x}{\sqrt{\sin x \cos x}}$

$\sqrt{2} \int \frac{(\sin x+\cos x) d x}{\sqrt{1-(1-\sin 2 x)}}$

$\sqrt{2} \int \frac{(\sin x+\cos x) d x}{\sqrt{1-(\sin x-\cos x)^{2}}}$

$\sqrt{2} \sin ^{-1}(\sin x-\cos x)+c$

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