If _ ^ f(x) ;dx x = x , then f(x) = - Vidyadip

MCQ

If $\int_{}^{} {\frac{{f(x)\;dx}}{{\log \sin x}} = \log \log \sin x} $, then $f(x) = $

A
$\sin x$
B
$\cos x$
C
$\log \sin x$
✓
$\cot x$

✓

Answer

Correct option: D.

$\cot x$

d
(d)$\int_{}^{} {\frac{{f(x)\,dx}}{{\log \sin x}}} = \log \log \sin x$
Differentiating both sides, we get
$\frac{{f(x)}}{{\log \sin x}} = \frac{{\cot x}}{{\log \sin x}} \Rightarrow f(x) = \cot x.$

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