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Question

If y=cos2(45+x)+(sinxcosx)2, where x(0,π2], then the possible value(s) of y is/are

A
0
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B
32
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C
3
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D
1
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Solution

The correct option is D 1
cos2(45+x)+(sinxcosx)2=(cos45cosxsin45sinx)2+(1sin2x)
=[cosx2sinx2]2+(1sin2x)=(1sin2x)2+(1sin2x)
=32(1sin2x)
As,
0<xπ20<2xπ0sin2x10sin2x11sin2x001sin2x1032(1sin2x)32y[0,32]

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