यदि ` y= tan^(-1). (cosx)/(1+ sin x) ,` हो तो `(dy)/(dx)` ज्ञात कीजिए ।

Explanation

क्योकि ` cos x = sin ( 1/2 pi - x) "और " sin x = cos ( 1/2 pi - x) `
अतः ` y = tan^(-1) . sin(1/2 pi - 2)/ ( 1=cos ( 1/2 pi - x))`
` tan ^(-1). ( 2sin (pi/4-x/2) cos ( pi/4 - x/2) )/ (2 cos^(2) ( pi/4- x/2))`
` = tan ^(-1) { tan (pi/4- x/2)}= pi/4-pi/2`
` (dy)/(dx) = d/(dx) ( pi/ 4) + d/(dx) (-x/2) = 0 -1/2 = -1/2 .`