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The function f(theta) = cos (pi sin^(2) ...

The function `f(theta) = cos (pi sin^(2) theta)`, is

A

not periodic

B

periodic and its period is same as that of `cos theta `

C

periodic and its period is same as that of ` cos 2 theta `

D

periodic and its period is same as that of ` cos ( pi theta)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`f(theta) = cos(pi sin^(2) theta)`
Clearly, `-pi le sin^(3) theta le pi` for ` theta in [-pi//2,pi//2]` and cosine function is an even function.
Same as the period of cos `2 theta`
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