y = sin (sin x) $\frac{dy}{dx}$ = cos (sin x) . cos x $\frac{d^2y}{dx^2}$ = cos (sin x) - . (- sin x) + cos x . (- si (sin x). cos x) $\frac{d^2y}{dx^2}$ = - sin x . cos (sin x) - y $\cos^2$ x now, $\frac{d^2y}{dx^2}$ + tan x $\frac{dy}{dx}$ + y $\cos^2$ x = - sin x . cos (sin x) - y $\cos^2$ x + tan x . cos (sin x) . cos x + y $\cos^2$ x = - sin x . cos (sin x) - y $\cos^2$ x + $\frac{\sin x}{\cos x}$ . cos (sin x) . cos x + y $\cos^2$ x = 0