Question

Differentiate `tan^(-1) ((1+cosx)/(sin x))` with respect to x

Answer 1

Let y = `tan^(-1) (1+cosx)/(sin x)` Then

`=> y = tan^(-1) ((2cos^2 x/2)/(2sin  x/2,cos  x/2))`

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

`=> y = tan^-1 {tan (pi/2 - x/2)}`

`=> y = pi/2 -pi/2`

`∴ (dy)/(dx) = 0 - 1/2 = - 1/2`