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Question

The derivative of tan−1[sinx1+cosx] with respect to tan−1[cosx1+sinx] is

A
2
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B
1
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C
0
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D
2
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Solution

The correct option is C 1
We have,
y1=tan1(sinx1+cosx)=tan1⎜ ⎜2sinx2cosx21+2cos2x21⎟ ⎟=tan1(tanx2)y1=x2dy1dx=12y2=tan1(cosx1+sinx)dy2dx=12(1+sinx).(1+sinx)=12dy1dx.dxdy2=12×2dy1dy2=1Hence,optionBiscorrectanswer.

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