If `x+y=pi+z,` then prove that `sin^2x+sin^2y-sin^2z=2 sinx siny cos z.`

If x+y+z= (pi)/(2) show that sin 2x + sin 2y + sin 2z =4 cos x cosy cos z

If cos x = tan y, cos y = tan z and cos z = tan x, prove that sin x = sin y = sin z = sin18 ^ (@)

Show that sin(x+y)sin(x-y)= sin^2 x -sin^2 y .Hence prove that sin(x+y)sin(x-y)+sin(y+z)sin(y-z) +sin(z+x)sin(z-x)=0

IF sin^(-1) X+ sin^(-1) y+ sin^(-1) z= pi , then prove that x^4 +y^4+ z^4 +4x^2 y^2 z^2 = 2(x^2 y^2 +y^2 z^2+z^2x^2).

If cos(y-z)+cos(z-x)+cos(x-y)=-3/2, prove that cos x + cos y + cos z = 0 = sin x + siny + sinz.

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

Prove that : sin (y + z-x) + sin (z + x-y) + sin (x +y-z)-sin (x+y+z) = 4 sin x sin y sin z .

If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=pi then prove that n xsqrt(1-x^(2))+ysqrt(1-y^(2))+zsqrt(1-z^(2))=2xy z

If sinx+siny+sinz=cosx+cosy+cosz=0, then (A) sin2x+sin2y+sin2z=0 (B) cos2x+cos2y+cos2z=0 (C) tanx+tany+tanz=0 (D) none of these