Phương pháp giải:

Sử dụng công thức: $\left\{ \begin{array}{l}\sin \left( {a + b} \right) = \sin a\cos b + \cos a\sin b\\\cos \left( {a + b} \right) = \cos a\cos b - \sin a\sin b\end{array} \right..$

Lời giải chi tiết:

$\begin{array}{l}\frac{{\sin \frac{\pi }{{15}}\cos \frac{\pi }{{10}} + \sin \frac{\pi }{{10}}\cos \frac{\pi }{{15}}}}{{\cos \frac{{2\pi }}{{15}}\cos \frac{\pi }{5} - \sin \frac{{2\pi }}{{15}}\sin \frac{\pi }{5}}} = \frac{{\sin \frac{\pi }{{15}}\cos \frac{\pi }{{10}} + \cos \frac{\pi }{{15}}\sin \frac{\pi }{{10}}}}{{\cos \frac{{2\pi }}{{15}}\cos \frac{\pi }{5} - \sin \frac{{2\pi }}{{15}}\sin \frac{\pi }{5}}}\\ = \frac{{\sin \left( {\frac{\pi }{{15}} + \frac{\pi }{{10}}} \right)}}{{\cos \left( {\frac{{2\pi }}{{15}} + \frac{\pi }{5}} \right)}} = \frac{{\sin \frac{\pi }{6}}}{{\cos \frac{\pi }{3}}} = 1.\end{array}$

Chọn C.