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^(m))/(y^(n))- (y^(n))/(x^(m))= 2i sin (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 xy - (1)/(xy) = 2i sin (alpha - beta)

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

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

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) .

If 2cos A=x+(1)/(x),2cos beta=y+(1)/(y) then show that 2cos(A-B)=(x)/(y)+(y)/(x)

2cos theta=x+(1)/(x) and 2cos phi=y+(1)/(y) then (A)x^(n)+(1)/(x^(n))=2cos(n theta)n in Z(B)(x)/(y)+(y)/(x)=2cos(theta-phi)(C)xy+(1)/(Xy)=2cos(theta+phi)(D)x^(m)y^(n)+(1)/(x^(m)y^(n))=2(cos m theta+n phi),m,n in Z

If x cos A + y sin A = m and x sin A - y cos A = n, then prove that : x^(2) + y^(2) = m^(2) + n^(2)

If (cos alpha)/(cos beta)=m and (cos alpha)/(sin beta)=n show that (m^(2)+n^(2))cos^(2)beta=n^(2)