tan^(-1)sqrt((1+sin(x)/(2)*2)/(1-sin(x)/(2)))

If y= tan ^(-1) sqrt (( 1 - sin x)/( 1 + sin x)) , then the vluae of (dy)/(dx) at x = pi /2 is

Prove that sin[2tan^(-1){sqrt((1-x)/(1+x))}]=sqrt(1-x^2)

int_(0)^(pi//2)tan^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]\ dx

If y=tan^(-1) [(sqrt(1+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin x)]] where 0 lt x lt pi/2 find (dy)/(dx)

If x=sin(2tan^(-1)2sqrt3)and y=sin((1)/(2)tan^(-1).(12)/(5)) , then

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)))

int(sin^(2)x*sec^(2)x+2tanx*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx= a) (cos^(2)x)(sin^(-1)x)+C b) (sin^(2)x)(sin^(-1)x)+C c) (sec^(2)x)(cos^(-1)x)+C d) (sec^(2)x)(tan^(-1)x)+C

int(sin^(2)x*sec^(2)x+2tan x*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx

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