Question

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

• A. $si{n}^{2}x.sin(cosx)$
• B. $si{n}^{2}xcos(sinx)$
• C. $co{s}^{2}x.sin(\cos x)$
• D. $co{s}^{2}xsin(sinx)$

Answer 1

Answer: (D)

$\frac{dy}{dx}=\cos (\sin x).\cos x$
$\Rightarrow$ $\frac{d^{2}y}{d{x}^2}=-\cos (\sin x).\sin x$
$+\cos [-\sin (\sin x)\cos x]$
$\Rightarrow$ $\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}\tan x=-{\cos }^{2}x.\sin (\sin x)$