Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\cos \left( {a + 2020\pi } \right) - 2\sin \left( {a - 7\pi } \right) - \cos \dfrac{{3\pi }}{2} - \cos \left( {a + \dfrac{{2019\pi }}{2}} \right) + \cos \left( {a - \dfrac{{3\pi }}{2}} \right).\cot \left( {a - 8\pi } \right)\\
= \cos \left( {a + 2.1010\pi } \right) - 2\sin \left[ {\left( {a - \pi } \right) - 3.2\pi } \right] - 0 - \cos \left[ {\left( {a - \dfrac{\pi }{2}} \right) + 2.505\pi } \right] + \sin \left[ {\dfrac{\pi }{2} - \left( {a - \dfrac{{3\pi }}{2}} \right)} \right].\cot \left( {a - 8\pi } \right)\\
= \cos a - 2\sin \left( {a - \pi } \right) - \cos \left( {a - \dfrac{\pi }{2}} \right) + \sin \left( {2\pi - a} \right).\cot a\\
= \cos a + 2\sin \left( {\pi - a} \right) - \cos \left( {\dfrac{\pi }{2} - a} \right) + \sin \left( { - a} \right).\dfrac{{\cos a}}{{\sin a}}\\
= \cos a + 2\sin a - \sin a - \sin a.\dfrac{{\cos a}}{{\sin a}}\\
= \cos a + 2\sin a - \sin a - \cos a\\
= \sin a
\end{array}\)
