If `cos^(-1) x +cos^(-1)y +cos^(-1)z =pi`, then prove that
`x^(2)+y^(2)+z^(2)+2xyz=1`.

If cos^-1 x +cos^-1 y + cos ^-1 z=pi , prove that x^2+y^2+z^2+2xyz=1 .

If "cos"^(-1)(x)/(a)+"cos"^(-1)(y)/(b) =theta , then prove that (x^(2))/(a^(2)) -(2xy)/(ab) cos theta +(y^(2))/(b^(2))=sin^(2) theta .

If sin^-1 x+sin^-1 y +sin^-1 z=pi/2 , prove that x^2+y^2+z^2+2xyz=1 .

If sin^(-1) x +sin^(-1)y +sin^(-1) z =(3pi)/(2) , then find the value of x^(100) +y^(100) +z^(100) -(9)/(x^(101)+y^(101)+z^(101)) .

If x^(1/3)+y^(1/3)+z^(1/3)=0 , then prove that (x+y+z)^3=27xyz

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

If cos^-1 x+cos^-1 y=theta , prove that x^2+y^2-2xycostheta=sin^2theta

If tan^-1 x+tan^-1 y+tan^-1 z=pi , prove that x+y+z=xyz

If sin^-1 x+sin^-1 y+sin^-1 z=pi , prove that x^4+y^4+z^4+4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^2)

Prove that 2 cos^(-1)x =cos^(-1)(2x^(2)-1) .