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Question

Show that tan1(cosx1+sinx)=πpxq,π2<x<3π2.
Find the value of p and q

A
p=2,q=3
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B
p=3,q=2
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C
p=2,q=4
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D
p=4,q=2
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Solution

The correct option is D p=4,q=2
tan1(cosx1+sinx)=tan1⎜ ⎜cos2x2sin2x2(cosx2+sinx2)2⎟ ⎟
=tan1⎜ ⎜cosx2sinx2cosx2+sinx2⎟ ⎟=tan1⎜ ⎜1tanx21+tanx2⎟ ⎟
=tan1tan(π4x2)=π4x2

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