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Question

The function f(x)=sin4x+cos4x increasing if

A
0<x<π/4
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B
π./4<x<3π/8
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C
3π/8<x<5π/8
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D
5π/8<x<3π/4
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Solution

The correct option is A 0<x<π/4
f(x)=sin4x+cos4x

f(x)=4sin3xcosx4cos3xsinx

f(x)=4sinxcosx(sin2xcos2x)=0

sinxcosx=0,sin2xcos2x=0

sinx=0,x=0

cosx=0,x=π2

sin2xcos2x=0x=π4

[π4,π2],f(π3)+f(x) is increasing.

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