For 0<x<2, d(tan-1(1+cos121-cos12)dxis equal to
-14
14
-12
12
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)