ddxcos-1cosx
12(secx+1)
(secx+1)
-12(secx+1)
-(secx+1)
Explanation for the correct option:
Find the valueddxcos-1cosx:
ddxcos-1x=-11-x2
Given,
ddxcos-1cosx=-11-cosx×ddxcosx=-11-cosx×12cosx×ddxcosx=-11-cosx×12cosx×-sinx=sinx21-cosxcosx
Since sin2x+cos2(x)=1
ddxcos-1cosx=1-cosx1+cosx21-cosxcosx[∵sinx=1-cos2x=1-cosx1+cosx]
=12(secx+1)
Hence, option(A) is correct.