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

Given, curve is $y=x \sin x$ At $\quad x=\frac{\pi}{2}$, we have $y=\frac{\pi}{2}$ Slope of the tangent at $x=\frac{\pi}{2}$ From Eq. (i), we get $$ \begin{aligned} \frac{d y}{d x} &=\sin x+x \cos x \\ \Rightarrow \quad \frac{d y}{d x} &=1 \text { at } \frac{\pi}{2} \end{aligned} $$ Now, equation of tangent will be $$ \begin{aligned} &x-\frac{\pi}{2}=y-\frac{\pi}{2} \\ &\Rightarrow \quad x=y \end{aligned} $$ This will intersect $X$-axis at $(0,0)$. So, the subtangent will be $=\frac{\pi}{2}-0=\frac{\pi}{2}$