y^(x)=x^(sin y)

If (sin x)^Y = (sin y)^x , find dy/dx :

Find dy/dx when (sin x)^y = (sin y)^x

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

[x (cos y) / (x) + y (sin y) / (x)] y = [y (sin y) / (x) -x (cos y) / (x)] x ((dy) / (dx))

Prove that (i) 2 cos x cos y=cos (x+y)+cos (x-y) (ii) -2 . sin x sin y=cos (x+y)-cos (x-y) (iii) 2 sin x cos y=sin (x+y)+sin (x-y) (iv) 2 cos x sin y=sin (x+y)-sin (x-y)

If (x+y)=sin(x+y) then (dy)/(dx)=

Solve the following differential equations (x cos\ (y)/(x)+y sin\ (y)/(x))y\ dx=(ysin\ (y)/(x)-xcos\ (y)/(x))x\ dy

Solve the following differential equations (x cos\ (y)/(x)+y sin\ (y)/(x))y\ dx=(ysin\ (y)/(x)-xcos\ (y)/(x))x\ dy