Question

If $y=\sin \theta +\cos \theta ,$ then the value of $\frac{d^{2}y}{d{x}^2}+y$ is

• A. $\sin \theta +\cos \theta$
• B. $\sin \theta -\cos \theta$
• C. $\sin 2\theta$
• D. $0$

Answer 1

The correct option is D $0$

Given, $y=\sin \theta +\cos \theta$,
Differentiating with respect to $x$ we get,
$\frac{dy}{dx}=\cos \theta -\sin \theta$

Differentiating again with respect to $x$ we get,
$\frac{d^{2}y}{d{x}^2}=\frac{d}{dx}\left(\frac{dy}{dx}\right)=-\sin \theta -\cos \theta =-(\sin \theta +\cos \theta )=-y$
$\therefore \frac{d^{2}y}{d{x}^2}+y=0$