`sin^(- 1)x+sin^(- 1)y=cos^(- 1) (sqrt(1-x^2) sqrt(1-y^2)-xy)` if `x in [0,1], y in [0,1]`

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_1-xy=1

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

(dy)/(dx) if y=sin^(-1)x+sin^(-1)sqrt(1-x^(2)),x is 0 to 1

Prove that sin ^ (- 1) x + cos ^ (- 1) y = (tan ^ (- 1) (xy + sqrt ((1-x ^ (2)) (1-y ^ (2)))) ) / (y sqrt (1-x ^ (2)) - x sqrt (1-y ^ (2)))

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

y = sin^(-1)(x/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2))

(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

If sin^(-1)x + sin^(-1)y + sin^(-1)z =pi , prove that xsqrt(1 - x^(2)) + y sqrt(1 -y^(2)) + z sqrt(1-z^(2))= 2xyz .

If y = (sin^(-1) x)/(sqrt(1-x^2)) show that (1-x^2) y_2 - 3xy_1 - y =0