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Question

If y = tan1(1+sinx1sinx),π2<x<π, then dydx equals

A
12
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B
1
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C
12
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D
1
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Solution

The correct option is A 12
y=tan1 (1cos(π2+x)1+cos(π2+x))=tan1tan(π4+x2))(i)
Now, π2<x<π
π4<x2<π2
or π2<π4+x2<3π4
tan(π4+x2)=tan(π4+x2) ( in second quadrant)
=tan{π(π4+x2)}
From Eq.(i),
y=tan1tan{π(π4+x2)}
=π(π4+x2)
=3π4x2
(principal value of tan1 x inπ2 to π2)
dydx=12

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