Answer
See explanations.
Work Step by Step
Step 1. Given $y=(\pi sin(x))/x$, we have $y'=\frac{x\pi cos(x)-\pi sin(x)}{x^2}$ which represents the slope of the tangent lines to the curve.
Step 2. At $x=\pi$, the slope is $m_1=\frac{\pi\pi cos(\pi)-\pi sin(\pi)}{\pi^2}=1$
Step 3. At $x=-\pi$, the slope is $m_2=\frac{-\pi\pi cos(-\pi)-\pi sin(-\pi)}{\pi^2}=-1$
Step 4. As $m_1m_2=-1$, these two tangent lines are normal to each other or intersect at a right angle.
