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Question

If f(x)=cos2x+sin4xsin2x+cos4x for xR then f(2002) is equal to

A
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B
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C
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Solution

The correct option is A 1
Formula:- sin2x+cos2x=1

f(x)=cos2x+sin4xsin2x+cos4x
=1sin2+sin4x1cos2x+cos4x

=1sin2x(1sin2x)1cos2x(1cos2x)
=1sin2xcos21cos2xsin2x=1

f(2002)=1sin2(2002)cos2(2002)1cos2(2002)sin2(2002)=1

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