Đáp án:
$P=\dfrac{-3}{2}$
Giải thích các bước giải:
$P=\dfrac{8\cos^3a-2\sin^3a+\cos a}{2\cos a-\sin^3a}\\
=\dfrac{\dfrac{8\cos^3a}{\cos^3a}-\dfrac{2\sin^3a}{\cos^3a}+\dfrac{\cos a}{\cos^3a}}{\dfrac{2\cos a}{\cos^3a}-\dfrac{\sin^3a}{\cos^3a}}\\
=\dfrac{8-2\tan^3a+\dfrac{1}{\cos^2a}}{\dfrac{2}{\cos^2a}-\tan^3a}\\
=\dfrac{8-2\tan^3a+1+\tan^2a}{2(1+\tan^2a)-\tan^3a}\\
=\dfrac{8-2.2^3+1+2^2}{2(1+2^2)-2^3}\\
=\dfrac{8-2.8+1+4}{2.5-8}\\
=\dfrac{-3}{2}$
