cot-1[1-sinx+1+sinx][1-sinx-1+sinx]=?
π-x
2π-x
x2
π-x2
Explanation for the correct option:
Given, cot−11−sinx+1+sinx1−sinx−1+sinx
By rationalizing it, we get
=cot−11−sinx+1+sinx1−sinx−1+sinx×1−sinx+1+sinx1−sinx+1+sinx
=cot−11−sinx+1+sinx21−sinx−1+sinx
=cot−11−sinx+1+sinx+21-sin2x1−sinx−1-sinx
=cot−12+2cos2x-2sinx
=cot−11+cosx-sinx
=cot−11+2cos2x2-1-2sinx2cosx2 ; ∵cosx=2cos2x2-1,sinx=2sinx2cosx2
=cot−1cosx2-sinx2
=cot−1−cotx2
=cot−1cotπ−x2 ; ∵cot(π-x2)=-cotx2
=π−x2
Hence, Option ‘D’ is Correct.