Question

The subtangent at $x=\pi /2$ on the curve $y=x\sin x$ is

• A. $0$
• B. $1$
• C. $\pi /2$
• D. None of these

Answer 1

The correct option is C $\pi /2$

Given curve is $y=x\sin x$ ... $\left(i\right)$

At $x=\frac{\pi }{2}$ we have $y=\frac{\pi }{2}$

Slope of the tangent at $x=\frac{\pi }{2}$

Form $\left(i\right)$

$\frac{dy}{dx}=\sin x+x\cos x$

$⟹\frac{dy}{dx}=1$ at $\frac{\pi }{2}$

Equation of tangent will be,



$x-\frac{\pi }{2}=y-\frac{\pi }{2}$

$⟹x=y$

This will intersect $x$ axis at $(0,0)$.

So, the sub-tangent will be $=\frac{\pi }{2}-0=\frac{\pi }{2}$