The sum of the absolute maximum and absolute minimum values of the function f x = tan - 1 sin x - cos x in the interval 0 , π is

Step-by-step solution

Given, f x = tan - 1 sin x - cos x Now differentiating the function we get, f ' x = cos x + sin x sin x - cos x 2 + 1 Now equating f ' x = 0 to find critical points, cos x + sin x sin x - cos x 2 + 1 = 0 ⇒ cos x + sin x = 0 ⇒ tan x = - 1 ∴    x = 3 π 4 Now checking the value of function at critical point and boundary point we get, x 0 3 π 4 π f x - π 4 tan - 1 2 π 4 So, we get, f x max = tan - 1 2 ∴   f x min = - π 4 So, the sum will be =