If `sin^(-1) x + sin^(-1) y = pi/2`, prove that `x sqrt(1-y^2) + y sqrt(1-x^2) =1`.

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that: xsqrt(1-x^2)+ysqrt(1-y^2)+zsqrt(1-z^2)=2x y z

if, sin^-1x + sin^-1y + sin^-1z =pi then prove that xsqrt(1-x^2) + ysqrt(1-y^2) + zsqrt(1-z^2) =2xyz.

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

(i) If sin ^(-) x + sin ^(-1) y = pi//2 , then prove that : cos^(-1) x = sin^(-1) y (ii) Prove that : sin ((1)/(2) cos^(-1).(4)/(5))= (1)/sqrt(10) (iii) Prove that : tan ((1)/(2) cos^(-1).(sqrt(5))/(3)) = (3-sqrt(5))/(2)

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

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that x^(2)-y^(2)+z^(2)-2xz sqrt(1-y^(2))=0

If sin^-1 x + sin^-1 y = (2pi)/3, then cos^-1 x + cos^-1 y =

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))

If y=(sin^(-1)x)^2 , prove that (1-x^2)y_2-x y_1-2=0 .