" (ii) "(sin y)^(x)=(cos x)^(y)

If tan(7x^(@))=(sin x^(@)cos y^(@)+cos x^(@)sin y^(@))/(cos x^(@)cos y^(@)-sin x^(@)sin^(@)) where x+y=134^(@) ,then the least positive integral value of x, is-

If (sin x)^(y)=(cos y)^(x), prove that (dy)/(dx)=(log cos y-y cot x)/(log sin x+x tan y)

If (sin x)^(y)=(cos y)^(x), prove that (dy)/(dx)=(log cos y-y cot x)/(log sin x+x tan y)

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

(dy) / (dx) = (sin x-sin y) (cos x) / (cos y)

The solution of the differential equation (dy)/(dx)+(sin2y)/(x)=x^(3)cos^(2)y

cos (x + y), sin (x + y), - cos (x + y) sin (xy), cos (xy), sin (xy) sin2x, 0, sin2y] | = sin2 (x + y)

Prove that :(sin x-sin y)/(cos x+cos y)=tan((x-y)/(2))

Prove that :(sin x+sin y)/(cos x+cos y)=tan((x+y)/(2))