Which of the following functions is decreasing on (0, 2 ) ? - Vidyadip

MCQ

Which of the following functions is decreasing on $\left(0, \frac{\pi}{2}\right)$ ?

A
$\sin 2 x$
B
$\tan x$
✓
$\cos x$
D
$\cos 3 x$

✓

Answer

Correct option: C.

$\cos x$

(c) : $f(x)=\cos x \Rightarrow f^{\prime}(x)=-\sin x$
In interval $\left(0, \frac{\pi}{2}\right), \sin x$ is positive
$
\therefore \quad f^{\prime}(x)<0 \forall x \in\left(0, \frac{\pi}{2}\right)
$
$\therefore f(x)$ is decreasing in $\left(0, \frac{\pi}{2}\right)$

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