cos^(-1)(xy-sqrt(1-x^(r))sqrt((-y^(2)))

Cos^(-1)(xy-sqrt(1-x^(2))sqrt(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]

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]

Q.tan^(^^)-1x+tan^(^^)-1y=pi+tan^(^^)-1((x+y)/(1-xy)) if x,y>0 and xy>0Q*cos^(^^)-1x+cos^(^^)-1y=2pi-cos^(^^)-1(xy-sqrt(1-x^(^^)2)sqrt(1-y^(^^)2)) if x+y<0

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

Differentiate tan^(-1)((sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))) w.r.t. cos^(-1)x^(2) .

underset0 If y=cos^(-1){x sqrt(1-x)+sqrt(x)sqrt(1-x^(2))} and

If y=cos^(-1){x sqrt(1-x)+sqrt(x)sqrt(1-x^(2))} and 0

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