Question

If y = sin (sin x) and $\frac{d^{2}y}{dx^{2}} + \frac{dy}{dx}$ tan x + ѓ(x) = 0, then ѓ(x) equals

• A. sin² x sin (cos x)
• B. sin² x cos (sin x)
• C. cos² x sin (cos x)
• D. cos² x sin (sin x)

Answer 1

Answer: (D)

cos² x sin (sin x)

Answer 2

$\frac{dy}{dx}$ = cos (sin x) . cos x

\ $\frac{d^{2}y}{dx^{2}}$ = – cos (sin x) sin x + cos x (– sin (sin x)) cos x

̃ $\frac{d^{2}y}{dx^{2}}$ + $\frac{dy}{dx}$ tan x = – cos (sin x) sin x – cos² x sin

(sin x) + cos (sin x) sin x

= – cos² x sin (sin x)

̃ $\frac{d^{2}y}{dx^{2}}$+ $\frac{dy}{dx}$ tan x + cos² x sin (sin x) = 0

̃ ƒ(x) = cos²x sin (sin x).