Simplify `tan^(-1).(cosx/(1-sinx))(-pi)/2 lt x lt pi/2`

Simplify tan^-1 (cosx/(1-sinx)) , for (-3pi)/2 < x< pi/2' .

Solve : tan^(-1)((cos x)/(1+sin x)) , -(pi)/(2) lt x lt (pi)/(2)

tan^(-1)(secx+tanx),(-pi)/(2) lt x lt (pi)/(2)

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

Express each of the following in the simplest form: tan^(-1){(cosx)/(1-sinx)} ,where -pi/2 < x < pi/2 (ii) tan^(-1)((cosx-sinx)/(cosx+sinx)) , -pi/4 < x < pi/4

Write the simplest form of tan^(-1)((cosx-sinx)/(cosx+sinx)), 0 lt x lt (pi)/(2)

If f(x) = tan^(-1)(sqrt((1+sinx)/(1-sinx))), 0 lt x lt pi/2 , then f'(pi/6) is

If f(x) = tan^(-1)(sqrt((1+sinx)/(1-sinx))), 0 lt x lt pi/2 , then f'(pi/6) is