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  4. The equation of the normal to the curve y=x2+ sin x cos x at the origin is

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Q. The equation of the normal to the curve $y=x^{2}+\sin x \cos x$ at the origin is

KCETKCET 2022

Solution:

$y = x ^{2}+\frac{\sin 2 x}{2}$
At $(0,0) \frac{d y}{d x}=2 x+\cos 2 x=2.0+\cos 0=1$
The equation of normal is $(y-0)=-1(x-0)$ or $x+y=0$