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Question

For 0<x<2, d(tan-1(1+cos121-cos12)dxis equal to


A

-14

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B

14

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C

-12

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D

12

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Solution

The correct option is A

-14


Explanation for the correct option :

Step1. Simplifying the given equation

Let, y=tan-11+cosx21-cosx2...(i) (1+cos2x)=2cos2x(1-cos2x)=2sin2x

Now using the above cos formula.

1+cosx2=2cos2x4&1-cosx2=2sin2x4

Insert this in equation (i)

Now,

y=tan-12cos2(x4)2sin2(x4)=tan-1cot2(x4)=tan-1[cot(π2-x4)=tan-1(tan(π2-x4))=π2-x4=-x4

Step3. Finding differentiation

Therefore, dydx=-14

Hence, correct option is (A)


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