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tan^(-1) [(cos x)/(1-sinx)]...

`tan^(-1) [(cos x)/(1-sinx)]`

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tan^(-1)((cos x)/(1-sin x))

tan^(-1)((cos x)/(1+sin x))

The derivative of tan^(-1)[(sin x)/(1+ cosx)] with respect to tan^(-1)[(cosx)/(1+sinx)] is

At x=(pi)/(4),(d)/(dx)[tan^(-1)((cosx)/(1+sinx))]=

tan^(-1)((1-cos x)/(sin x))

Express each of the following in the simplest form: tan^(-1){(cosx)/(1-sinx)},\ -pi/2

Derivative fo tan^(-1)((sinx)/(1+cosx))w.r.t.tan^(-1)((cosx)/(1+sinx)) is

tan^-1(cosx/(1-sinx))

Prove that tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)