The period of the function sin3 ⁡x2+cos5⁡ x5 is

f(x)=sin3 ⁡x2+cos5⁡x5 The period of sin3⁡ x is 2π So, the period of sin3 ⁡x2 is 2π1/2=4π So, the period or sin3 ⁡x2 is 2π The period of cos5⁡x is 2π So, the period of cos5⁡ x5 is 2π15=10π So, the period of cos5⁡ x2 is 5π Now, period of f(x)=LCM of {2π,5π}=10π

The period of the function sin3 ⁡x2+cos5⁡ x5 is

f(x)=sin3 ⁡x2+cos5⁡x5 The period of sin3⁡ x is 2π So, the period of sin3 ⁡x2 is 2π1/2=4π So, the period or sin3 ⁡x2 is 2π The period of cos5⁡x is 2π So, the period of cos5⁡ x5 is 2π15=10π So, the period of cos5⁡ x2 is 5π Now, period of f(x)=LCM of {2π,5π}=10π

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The period of the function $|\sin^{3} \frac{x}{2}| + |\cos^{5} \frac{x}{5}|$ is

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$2 π$

$10 π$

$8 π$

$5 π$

answer is B.

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Detailed Solution

$f (x) = |\sin^{3} \frac{x}{2}| + |\cos^{5} \frac{x}{5}| The period of \sin^{3} x is 2 π So, the period of \sin^{3} \frac{x}{2} is \frac{2 π}{1 / 2} = 4 π So, the period or |\sin^{3} \frac{x}{2}| is 2 π The period of \cos^{5} x is 2 π So, the period of \cos^{5} \frac{x}{5} is \frac{2 π}{(\frac{1}{5})} = 10 π So, the period of |\cos^{5} \frac{x}{2}| is 5 π Now, period of f (x) = LCM of {2 π, 5 π} = 10 π$