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