A calculus problem by Pratik Shastri

Calculus Level 4

$\large \dfrac{\displaystyle\int_{0}^{\pi/2} \sin^{100} x \, dx}{\displaystyle\int_{0}^{\pi/2} \sin^{102} x \, dx}$

If the integral above can be expressed as $\dfrac ab$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .