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Question

If f(x)=sin4x+cos4x12sin2x, then the range of f(x) is

A
[0,32]
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B
[12,72]
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C
[0,98]
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D
[34,78]
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Solution

The correct option is C [0,98]
Given : f(x)=sin4x+cos4x12sin2x
f(x)=12sin2xcos2x12sin2xf(x)=1sin22x2sin2x2f(x)=sin22x+sin2x22f(x)=(sin2x+12)2942

We know that,
1sin2x112sin2x+12320(sin2x+12)29498(sin2x+12)294200(sin2x+12)2+94298f(x)[0,98]

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