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Question

Fundamental period of f(x)=sin4x+cos4x is

A
π2
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B
π
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C
2π
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D
3π2
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Solution

The correct option is A π2
Let f(x)=sin4x+cos4x
=(sin2x+cos2x)22sin2xcos2x=14sin2xcos2x2=1sin22x2=114(2sin22x)=1(1cos4x4)=34+14cos4x
fundamental period of cosx=2π
Hence, fundamental period of function =2π4=π2

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