The period of the function $$f(x)=$$$$cos$$⁡$$x2+$$|$$sin$$⁡x| is kπ, then k is equal to

We know that $$sin$$ x and $$cos$$ x are periodicfunctions each with period π. Therefore, $$cos$$⁡$$x2$$ is periodic with period $$2$$π Thus, $$f(x)=$$$$cos$$⁡$$x2+$$|$$sin$$⁡x| is periodic with period $$2$$π ∴ kπ$$=2$$π⇒$$k=2$$.

Extreme values and Periodicity of Trigonometric functions

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The period of the function $f (x) = |\cos \frac{x}{2}| + | \sin x |$ is $kπ$ , then k is equal to

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Solution

We know that $|\sin x|$ and $|\cos x|$ are periodic
functions each with period $π$ . Therefore, $|\cos \frac{x}{2}|$ is periodic with period 2 $π$
Thus, $f (x) = |\cos \frac{x}{2}| + | \sin x |$ is periodic with period 2 $π$
$∴ k π = 2 π \Rightarrow k = 2 .$

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