Giải thích các bước giải:
1.Ta có:
$\dfrac{\pi}{2}<\alpha<\pi$
$\to \sin\alpha>0$
Mà $\sin^2\alpha=1-\cos^2\alpha=\dfrac14$
$\to \sin\alpha=\dfrac12$
$\to\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=-\dfrac{1}{\sqrt3}$
$\to\cot\alpha=\dfrac1{\tan\alpha}=-\sqrt3$
2.Ta có:
$\pi<\alpha<\dfrac32\pi$
$\to \cos\alpha<0$
Mà $\dfrac1{\cos^2\alpha}=1+\tan^2\alpha=\dfrac{41}{25}$
$\to\cos\alpha=-\dfrac{5}{\sqrt{41}}$
$\to \sin\alpha=\tan\alpha\cdot \cos\alpha=\dfrac{-4}{\sqrt{41}}$
Ta có: $\cot\alpha=\dfrac1{\tan\alpha}=\dfrac54$
