(sin x cos y=)/(1+a^(n-m))+(1)/(1+a^(m-n))

If y=(1)/(1+x^(n-m)+x^(p-m))+(1)/(1+x^(m-n)+x^(p-m))+(1)/(1+x^(m-p)+x^(n-p)) the (dy)/(dx) is

Simplify the following: 1/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(n-m)+x^(p-n))

Simplify : (1)/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(p-m)+x^(p-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 x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

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)