First slide

Functions (XII)

Question

$Period of f (x) = \cos (| \sin x | - | \cos x |) is$

Moderate

A

$π$
B

$2 π$
C

$\frac{π}{2}$
D

None of these

Solution

$l e t f (x) = \cos (|\sin x| - |\cos x|)$
$\Rightarrow f (\frac{π}{2} + x) = \cos (|\sin (\frac{π}{2} + x)| - |\cos (\frac{π}{2} + x)|)$
= $\cos (|\cos x| - |- \sin x|)$
$= \cos (|\sin x| - |\cos x|) \sin c e \cos (- x) = \cos x$
$= f (x)$
period of f(x) = $\frac{π}{2}$ since $\frac{π}{2}$ is the least positive value satisfying the above condition.

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