If `x=cos alpha+i sin alpha` and ` y=cos beta+i sin beta,z=cos gamma+i sin gamma` and if `x+y+z=0` then prove that `(1)/(x)+(1)/(y)+(1)/(z)=0`

If x=cos alpha+i sin alpha, y=cos beta+i sin beta then " (y)/(x)-(x)/(y)=

If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c = cos 2gamma + i sin 2 gamma . Prove that . sqrt(abc) + 1/(sqrt(abc)) = 2 cos (alpha + beta + gamma)

If alpha=cos alpha+i sin alpha,b=cos beta+i sin beta,c=cos gamma+i sin gamma and (b)/(c)+(c)/(a)+(a)/(b)=1 then cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=

If x= cos alpha+ i sin alpha, y = cos beta+ i sin beta, then prove that (x-y)/(x+y) =i (tan )(alpha-beta)/2

If a=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin gamma and b/c+c/a+a/b=1, then cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta) =

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta)=

If alpha,beta and gamma are angles such that tan alpha+tan beta+tan gamma=tan alpha tan beta tan gamma and x=cos alpha+i sin alpha,y=cos beta+i sin beta and z=cos gamma+i sin gamma then the value of xyz is

cos alpha sin (beta-gamma)+cos beta sin (gamma-alpha) +cos gamma(sin alpha-beta)=