[" (i) "x sqrt(1-y^(2))+y sqrt(1-x^(2))=1],[" (ii) "sin^(-1)x+sin^(-1)sqrt(1-x^(2))=(pi)/(2)]

sin ^(-1)sqrt(3)x+sin ^(-1)x=(pi)/(2)

solve : tan^(-1) sqrt(x(x+1))+sin ^(-1) (sqrt(1+x+x^(2)))=(pi)/(2)

If tan ^(-1) x + tan ^(-1) .sqrt( 1 - y^(2))/y = pi/3 " and sin^(-1) y - cos^(-1) ( x/(sqrt( 1 + x^(2)))) = (pi)/6 , then ( 5 sin^(-1) x)/( sin^(-1) y) is

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)), then prove that (dy)/(dx)=(sin^(-1)x)/((1-x^(2))^((3)/(2)))

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

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

If tan ^(-1) x + tan ^(-1) .sqrt( 1 - y^(2))/y = pi/3 " and " sin^(-1) y - cos^(-1) ( x/(sqrt( 1 + x^(2)))) = pi/6 " , then " ( 5 sin^(-1) x)/( sin^(-1) y) is

If tan ^(-1) x + tan ^(-1) .sqrt( 1 - y^(2))/y = pi/3 " and " sin^(-1) y - cos^(-1) ( x/(sqrt( 1 + x^(2)))) = pi/6 " , then " ( 5 sin^(-1) x)/( sin^(-1) y) is

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

Find (dy)/(dx), if y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]