\[\int_{0}^{\pi/2}(\cos t)^{a-1}\cos\left(bt\right)\,\mathrm{d}t=\frac{\pi}{2^{a%
}}\frac{1}{a\mathrm{B}\left(\frac{1}{2}(a+b+1),\frac{1}{2}(a-b+1)\right)},\]