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Question

(sin xcosx)2+cos2(π4+X)

A
[0,1
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B
[0,2]
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C
[1,2]
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D
[0,3]
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Solution

The correct option is D [0,3]
f(x)=(sinxcosx)2+cos2(π4+x)
=12sinxcosx+cos2(π4+x)

=1sin2x+1+cos(π2+2x)2
=22sin2x+1sin2x2[2cos2x1=cos2x]
=33sin2x2
f(x)=32(1sin2x)
Range of sin2xϵ[1,1]
Range of f(x)ϵ[0,3]

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