Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{{\sin 2a + \sin 5a - \sin 3a}}{{1 + \cos a - 2{{\sin }^2}2a}}\\
= \dfrac{{\sin 2a + \left( {\sin 5a - \sin 3a} \right)}}{{\cos a + \left( {1 - 2{{\sin }^2}2a} \right)}}\\
= \dfrac{{\sin 2a + 2.cos\dfrac{{5a + 3a}}{2}.\sin \dfrac{{5a - 3a}}{2}}}{{\cos a + \cos 4a}}\\
= \dfrac{{2\sin a.\cos a + 2\cos 4a.\sin a}}{{\cos a + \cos 4a}}\\
= \dfrac{{2\sin a.\left( {\cos a + \cos 4a} \right)}}{{\cos a + \cos 4a}}\\
= 2\sin a
\end{array}\)
