If `cosy = x cos(a+y)`, then prove that `(dy)/(dx)=cos^2(a+y)/(sina)` where cos `a where `cos ane+-1` .

If sin y = x cos (a + y) , prove that (dy)/(dx) = (cos^2 (a + y))/(cos a)

If cosy = xcos(a+y) , with cos a ne +-1 , prove that dy/dx = (cos^2(a+y))/sina

If x sin (a+y) + sin a cos (a+y) = 0, then prove that : dy/dx = (sin^2(a+y))/(sina)

If y = x sin y, prove that x dy/dx = y/(1-x cosy)

Solve (dy)/(dx)+2y=cos x.

If y = 2 sin x + 3 cos x, prove that y + (d^2y)/(dx^2) = 0

If y = 2 cos x -6 sin x , prove that (d^2y)/(dx^2)+y = 0

If x cos (a+y) = cos y, then prove that dy/dx = (cos^2(a+y))/(sina) Hence, show that sina(d^2y)/(dx^2)+ sin 2(a+y) (dy)/(dx) = 0

If x cos (a + y)=cos y then prove that [dy/dx = cos^2 (a+ y) /sin a] . Hence show that [sin a (d^2y /dx^2) + sin 2(a+ y) dy/dx =0] .