" 18."tan^(-1)sqrt((1+sin x)/(1-sin x))=(pi)/(4)+(x)/(2)

sqrt((1+sin x)/(1-sin x))=tan((pi)/(4)+(x)/(2))

Differentiate the following functions with respect to x:tan^(-1){sqrt((1+sin x)/(1-sin x))},-(pi)/(2)

Differentiate the following functions with respect to x:tan^(-1){sqrt((1+sin x)/(1-sin x))},-(pi)/(2)

Prove that tan^(-1)((cosx)/(1+sin x)) =(pi)/(4)-(x)/(2), x in (-(pi)/(2), (pi)/(2)) .

If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2) then f' ((pi)/(6)) =?

If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2) then f' ((pi)/(6)) =?

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1

Evaluate int tan^(-1) { sqrt((1-sin x)/(1+ sin x ))} dx , -pi/2 lt x lt pi/2

Prove that : cot^(-1)(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))=(x)/(2),0

If x in(pi,(3 pi)/(2)) then the value of tan^(-1)((sqrt(1-sin x)+sqrt(1+sin x))/(sqrt(1-sin x)-sqrt(1+sin x)))