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Question

The value of sin2x0sin1(t)dt+cos2x0cos1(t)dt is


A

π4

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B

0

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C

π2

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D

None of these

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Solution

The correct option is A

π4


Let f(x)=sin2x0sin1(t)dt+cos2x0cos1(t)dt
Here f(x)=0 f(x)=c (a constant).
But f(π4)=120(sin1t+cos1t)dt=120(π2)dt=π4


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