If `"sin"^(-1) (x)/(a)+"sin"^(-1)(y)/(b)="sin"^(-1)(c^(2))/(ab)`, prove that,
`b^(2)x^(2)+2xy sqrt(a^(2)b^(2)-c^(4))+a^(2)y^(2)=c^(4)`

sin ^(-1)""(ax)/(C ) +sin ^(-1) ""(bx)/(c ) =sin ^(-1)""x where a^(2)+b^(2)=c^(2) and c ne 0

if cos ^(-1 ) ""(x )/(a) + cos ^(-1 )""(y)/(b ) = alpha prove that , (x^(2) )/(a^(2)) -(2xy)/(ab ) ""cos alpha +(y^(2))/(b^(2))= sin ^(2) alpha

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

"if " sin^(-1) x +sin ^(-1) y+sin ^(-1) z=pi show that , x^(4)+y^(4)+z^(4)+4x^(2)y^(2)z^(2)=2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2))

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

sin ^(-1) ""(2a)/(1+a^(2))+sin ^(-1) ""(2b)/(1+b^(2) ) = 2 tan ^(-1) x

(x) (a sin(B-C))/(b^(2)-c^(2)) = (b sin (C-A))/(c^(2)-a^(2)) = (c sin(A-B))/(a^(2)-b^(2))

If a sin x=b cosx=(2c tan x)/(1-tan^(2)x) , then prove that (a^(2)-b^(2))^(2)=4c^(2)(a^(2)+b^(2)).

If (sin A)/(sin C) = (sin (A-B))/(sin (B-C)) , then show that, a^(2), b^(2), c^(2) are in A.P.

Prove that ("sin"^(-1)(2ab)/(a^(2)+b^(2))+"sin"^(-1)(2cd)/(c^(2)+d^(2))) can be expressed in the form "sin"^(-1)(2xy)/(x^(2)+y^(2)) where x and y are rational functions of a,b,c and d.