`(cosx)^(y)=(siny)^(x)`

(cosx)/(cosy)=n,(sinx)/(siny)=m , then (m^(2)-n^(2))sin^(2)y=?

(cosx+cosy)^(2)|(sinx-siny)^(2)=4cos^(2)(x+y)/(2)

Prove that : (cosx-cosy)^(2)+(sinx-siny)^(2)=4sin^(2)""(x-y)/(2)

Prove that : (cosx+cosy)^(2)+(sinx-siny)^(2)=4cos^(2)""(x+y)/(2)

Prove that (cosx+cosy)^(2)+(sinx-siny)^(2)=4cos^(2)((x+y)/(2))

If (sinx)/(siny)=(1)/(2),(cosx)/(cosy)=(3)/(2) , where x,y in (0,(pi)/(2)) , then the value of tan (x+y) is equal to

(cosx-cosy)^(2)+(sinx-siny)^(2)=?

If y^(cosx)=x^(siny)," then "(dy)/(dx)=