Differentiate the following functions with respect to `x` : `tan^(-1){sqrt((1+cosx)/(1-cosx))},0ltxltpi`

Explanation

y=`tan^(-1){sqrt((1+cosx)/(1-cosx))}`

y=`tan^(-1){sqrt((2cos^2(x/2))/(2sin^(x/2)))}`

=`tan^(-1)(cot(x/2))`

=`tan^(-1)(tan(pi/2-x/2))`

=`pi/2-x/2`

`dy/dx=-1/2`