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Standard XII

Mathematics

Basic Inverse Trigonometric Functions

The function ...

Question

The function $f (x) = | sin 4 x | + | cos 2 x |$ , is a periodic function with period

2 π

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π

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\frac{π}{2}

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\frac{π}{4}

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Solution

The correct option is C $\frac{π}{2}$
Given $f (x) = | sin 4 x | + | cos 2 x |$

$= \sqrt{{sin}^{2} 4 x} + \sqrt{{cos}^{2} 2 x}$

$= \sqrt{\frac{1 - cos 8 x}{2}} + \sqrt{\frac{1 + cos 4 x}{2}}$

Now, period of $= \sqrt{\frac{1 - cos 8 x}{2}}$ is $\frac{π}{4}$

Period of $= \sqrt{\frac{1 + cos 4 x}{2}}$ is $\frac{π}{2}$ .

LCM of $\frac{π}{4}$ and $\frac{π}{2}$ is $\frac{π}{2}$ .

Hence, period of $f (x)$ is $\frac{π}{2}$ .

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Similar questions

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The function f(x)=|sin4x|+|cos2x|, is a periodic function with period

The correct option is C π2Given f(x)=|sin4x|+|cos2x|=√sin24x+√cos22x=√1−cos8x2+√1+cos4x2Now, period of =√1−cos8x2 is π4Period of =√1+cos4x2 is π2.LCM of π4 and π2 is π2.Hence, period of f(x) is π2.

The function $f (x) = | sin 4 x | + | cos 2 x |$ , is a periodic function with period