If `x=sin(2tan^(-1)2)and y=sin((1)/(2)tan^(-1).(4)/(3))`, then prove that y^2 = 1 - x

If x=sin(2tan^(-1)3)and y=sin((1)/(2)tan^(-1)(4/3)) , then

sin (tan ^(-1)2x)

If x=sin(2tan^(- 1)2), y=sin(1/2tan^(- 1)(4/3)) , then -

If sin^(-1)x + tan ^(-1) x = (pi)/(2) , then prove that 2x^(2) + 1 = sqrt(5)

If y= "tan"^(-1) (4x)/(1+5x^(2)) + "tan"^(-1) (2 + 3x)/(3-2x) , then prove that (dy)/(dx)= (5)/(1+25x^(2))

If tan^(-1) x+tan^(-1)y+tan^(-1)z=pi/2 then prove that yz+zx+xy=1

If sin^(-1)x+tan^(-1)x=(pi)/(2) , prove that : 2x^(2)+1=sqrt(5)

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then prove that (1-x^2)y_2-xy_(1)-4=0.

If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}], find (dy)/(dx)

If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}], find (dy)/(dx)