If ` 2 cos alpha = x + 1/x, 2 cos beta = y + 1/y` then `x^10/y^12 - y^12/x^10 = `

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that xy - (1)/(xy) = 2i sin (alpha - beta)

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that x^(m) y^(n) + (1)/(x^(m)y^(n)) = 2 cos (m alpha + n beta)

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that (x)/(y) + (y)/(x) = 2 cos( alpha - beta)

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that (x^(m))/(y^(n))- (y^(n))/(x^(m))= 2i sin (m alpha - n beta)

If x + (1)/(x ) =2 sin alpha , y +(1)/(y) =2 cos beta , then x^3 y^3 + (1)/( x^3 y^3) is

If x+1/x=2cos alpha,y+1/y=2cos beta, then xy+(1)/(xy)=

If cos alpha =1/2(x+1/x),cos beta=1/2(y+1/y) then evaluate cos(alpha-beta)

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" (2(1-cos (alpha - beta)))/(cos beta - cos alpha)^(2)=

If x = cos alpha + i sin alpha , y = cos beta + i sin beta , prove that x^(m)y^(n)+1/(x^m y^n) = 2 cos (m alpha + n beta) .