Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
22.\\
A = \sin \left( {\dfrac{{13\pi }}{2} - a} \right) + \cos \left( {\dfrac{{15\pi }}{2} + a} \right)\\
= \sin \left( {6\pi + \left( {\dfrac{\pi }{2} - a} \right)} \right) + \cos \left( {8\pi + \left( {a - \dfrac{\pi }{2}} \right)} \right)\\
= \sin \left( {\dfrac{\pi }{2} - a} \right) + \cos \left( {a - \dfrac{\pi }{2}} \right)\\
= \sin \left( {\dfrac{\pi }{2} - a} \right) + \cos \left( {\dfrac{\pi }{2} - a} \right)\\
= \cos a + \sin a\\
24,\\
\tan a.\cot a = \dfrac{{\sin a}}{{\cos a}}.\dfrac{{\cos a}}{{\sin a}} = 1\\
{\tan ^3}a - {\cot ^3}a = \left( {\tan a - \cot a} \right)\left( {{{\tan }^2}a + \tan a.\cot a + {{\cot }^2}a} \right)\\
= \left( {\tan a - \cot a} \right)\left[ {{{\left( {\tan a - \cot a} \right)}^2} + 3\tan a.\cot a} \right]\\
= 6.\left( {{6^2} + 3.1} \right)\\
= 234
\end{array}\)
