Giải thích các bước giải:

Vì $0^o<a<180^o$

$\to \sin a>0, \cos a<0, \tan a<0, \cot a<0$

Ta có:

$\cos a=-\dfrac13$

$\to \cos^2a=\dfrac19$

$\to \dfrac1{\cos^2a}=9$

$\to \dfrac{\sin^2a+\cos^2a}{\cos^2a}=9$

$\to \dfrac{\sin^2a}{\cos^2a}+1=9$

$\to\tan^2a+1=9$

$\to\tan^2a=8$

$\to\tan a=-2\sqrt2$ vì $\tan a<0$

$\to \cot a=\dfrac1{\tan a}=\dfrac{-1}{2\sqrt2}$

$\to P=-2\sqrt2+2\cdot \dfrac{-1}{2\sqrt2}\approx -3.5$