The equation of the normal to the curve y = 2 sin x at (0, 0) is :

The correct answer is Option (4) → $x+2y = 0$

$y = 2 \sin x$ at (0, 0)

$\frac{dy}{dx}=2\cos x⇒\left.\frac{dy}{dx}\right]_{x=0}=2$

so slope of normal = $-\frac{1}{2}$

eq → $y=-\frac{1}{2}x⇒x+2y=0$