Cho góc alpha thỏa mãn cos alpha =-4/5 và pi <alpha<3 pi/ 2 . Tính tan (alpha - pi /4 Cần gấp ạ

`\text{Vì}` `\pi < \alpha < \frac{3\pi}{2}` `\text{nên sin}` `\alpha < 0`

`\text{Mặt khác, từ}` `sin^{2} \alpha + cos^{2} \alpha = 1`

`=> sin \alpha = - \sqrt{1 - (- \frac{4}{5})^{2}} = - \frac{3}{5}`

`=> tan \alpha = \frac{sin \alpha}{cos \alpha} = \frac{3}{4}`

`\text{Ta có:}` `tan (\alpha - \frac{\pi}{4}) = \frac{tan \alpha - tan \frac{\pi}{4}}{1 + tan \alpha.tan \frac{\pi}{4}}`

                                        `= - \frac{1}{7}`

` Vậy ` ______________________________________________________

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