[" Prove that "],[qquad sin^(-1)x+cos^(-1)y=tan^(-1)xy+sqrt(3)(1+x^(2))(10y^(2))^(3)]

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

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)))

prove that . Tan ^(-1) x- tan ^(-1 )y = cos ^(-1) (1+xy)/(sqrt((1+x^(2))(1+y^(2)))).

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]

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

Prove that xy tan^-1x+tan^-1y=tan^-1(frac(x+y)(1-xy))

Prove the following: sin^-1x-sin^-1y = sin^-1[x(sqrt(1-y^2))-y(sqrt(1-x^2))]

Prove that tan ^(-1)""(1)/(x+y)+ tan ^(-1)""(y)/(x^(2)+xy+1)= cot ^(-1)x.

Prove that tan^(-1)(1/(x+y))+tan^(-1)(y/(x^2+xy+1) )= cot^(-1)x .