Orthogonality and Inner Product Integrals

Question requiring computation of integrals of products of trigonometric or special functions to establish orthogonality relations or norms.

grandes-ecoles 2021 Q31 View

Let $( m , n ) \in \mathbb { N } ^ { 2 }$. Calculate $\int _ { 0 } ^ { \pi / 2 } \sin ( ( 2 m + 1 ) \theta ) \sin ( ( 2 n + 1 ) \theta ) \mathrm { d } \theta$.