Differentiate `tan^(-1){sqrt((1+cosx)/(1-cosx))}`,`0

Explanation

Given that,
`y=tan^(-1){sqrt((1+cosx)/(1-cosx))}`
`0ltxltpi`
`y=tan^-1 sqrt{(2cos^2(x/2))/(2sin^2(x/2))}`
`=>y=tan^-1 sqrt(cot^2(x/2))`
`=>y=tan^-1 [cot(x/2)]`
`=>y=tan^-1 [tan(pi/2-x/2)]`
`0ltxltpi`
`=>0ltx/2ltpi/2`
`=>0 lt pi/2-x/2 lt pi/2`
`y=pi/2-x/2`
`(dy)/(dx)=-1/2`