Differentiate `tan^(-1){(1-cosx)/(sinx)}`,`-piltxltpi` with respect to `x` :

Explanation

Given that,
`y=tan^(-1){(1-cosx)/(sinx)}`
`-piltxltpi`
`y=tan^-1 [(2sin^2 (x/2))/(2 sin( x/2 )cos (x/2))]`
`=>y=tan^-1 (tan(x/2))`
`-piltxltpi`
`=>-pi/2 lt x lt pi/2`
`y= x/2`
`(dy)/(dx) =1/2`