" (iii) "x^(m)y^(n)=x^(m)+y^(n)

" Find "(dy)/(dx)" if "x^(m)y^(n)=x^(m)+y^(n)

If x^(m)y^(n)=(x+y)^(m+n)

If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "x^(m).y^(n)+(1)/(x^(m).y^(n))

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 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)

Find (dy)/(dx) if x^(m)y^(n)=((x)/(y))^(m+n)

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 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 x=a^(m+n),y=a^(n+1) and z=a^(l+m) prove that x^(m)+y^(n)z^(l)=x^(n)y^(l)z^(m)

If x=a^(m+n),y=a^(n+1) and z=a^(l+m) prove that x^(m)+y^(n)z^(l)=x^(n)y^(l)z^(m)