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 \(a+b\).