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)`

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

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

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

If tan^-1 x+tan^-1 y+tan^-1 z=pi/2 , prove that xy+yz+zx=1

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

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

If x, y, z,w in are in G.P., prove that (xy-wz)/(y^2-z^2)=(x+z)/y .

Resolve into factors x^4(y^2-z^2)+y^4(z^2-x^2)+z^4(x^2-y^2)

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)) .