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Question

tan1[cosx1+sinx] is equal to

A
π4x2,forxϵ(π2,3π2)
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B
π4x2,forxϵ(π2,π2)
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C
π4x2,forxϵ(3π2,5π2)
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D
π4x2,forxϵ(3π2,3π2)
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Solution

The correct option is A π4x2,forxϵ(π2,3π2)
tan1[sin(π2x)1+cos(π2x)]
=tan1[2sin(π4x2).cos(π4x2)2cos2(π4x2)]
=tan1[tan(π4x2)]
=π4x2
where,
π2<π4x2<π2π2<x<3π2

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