If a = cos `alpha + isin alpha, b = - cos beta + isin beta ` then `(ab - (1)/(ab))` is _______

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

If p=cos2 alpha+isin2 alpha,q=cos2beta+isin2beta then sqrt(p//q)-sqrt(q//p)=

If p=cos2alpha+isin2alpha,q=cos2beta+isin2beta" then "sqrt(p//q)-sqrt(q//p)

If a = cos2alpha+isin2alpha , b= cos2 beta + i sin2 beta, c=cos2 gamma +isin2 gamma then prove that sqrt(abc)+(1)/(sqrt(abc))=2cos (alpha + beta+ gamma)

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)=

If ( cos 2 alpha+ isin 2alpha)(cos 2 beta+ isin 2 beta)= cos theta+isin theta , then find the value of theta .

The real part of |(cos alpha+isin alpha, cos beta+ i sin beta),(sin beta+i cos beta, sin alpha +icos alpha)| is

If (x) / (a) cos alpha + (y) / (b) sin alpha = 1, (x) / (a) cos beta + (y) / (b) sin beta = 1 and (cos alpha cos beta) / (a ^ (2)) + (without alpha without beta) / (b ^ (2)) = 0 then