Cho biết tan alpha= -4. Tính các giá trị lượng giác còn lại của góc alpha

$\text{Ta có:}$

$\text{+) tan$\alpha$.cot$\alpha$ = 1}$

$\text{→ cot$\alpha$ = $\frac{1}{tan\alpha}$ = -$\frac{1}{4}$}$ 

$\text{+) 1 + $tan^{2}\alpha$ = $\frac{1}{cos^{2}\alpha }$}$

$\text{⇔ 1 + (-4)² = $\frac{1}{cos^{2}\alpha }$}$

$\text{⇔ 17 = $\frac{1}{cos^{2}\alpha }$}$

$\text{⇔ $cos^{2}\alpha$ = $\frac{1}{17}$ }$

$\text{⇔ cos$\alpha$ = $\frac{\sqrt{17}}{17}$ }$

$\text{+) $sin^{2}\alpha$ + $cos^{2}\alpha$ = 1}$

$\text{⇔ $sin^{2}\alpha$ = 1 - $cos^{2}\alpha$}$

$\text{⇔ $sin^{2}\alpha$ = 1 - $(\frac{\sqrt{17}}{17}) ^{2}$ }$

$\text{⇔ $sin^{2}\alpha$ = $\frac{16}{17}$ }$

$\text{⇔ sin$\alpha$ = $\frac{4\sqrt{17}}{17}$ }$