Get the solution to "find the exact value of tan⁡(4π3−π4)"

Jaden Easton

Answered question

2021-08-20

find the exact value of $\tan (\frac{4 π}{3} - \frac{π}{4})$

Alix Ortiz

Skilled2021-08-21Added 109 answers

Trigonometry:

$\tan (\frac{4 π}{3} - \frac{π}{4})$

We know

$\tan (a - b) = \frac{\tan a - \tan b}{1 + \tan a \tan b}$

$\tan (\frac{4 π}{3}) = \tan (240^{\circ})$

$= \tan (90 \cdot 2 + 60^{\circ})$

$= \tan 60^{\circ}$

$= \sqrt{3}$

$\tan (\frac{π}{4}) = 1$

$\tan (\frac{4 π}{3} - \frac{π}{4})$

$= \frac{\tan \frac{4 x}{3} - \tan \frac{x}{4}}{1 + \tan \frac{4 x}{3} \tan \frac{x}{4}}$

$= \frac{\sqrt{3} - 1}{1 + \sqrt{3}}$

$= \frac{(\sqrt{3} - 1) (\sqrt{3} - 1)}{(\sqrt{3} + 1) (\sqrt{3} - 1)}$

$= \frac{3 - 2 \sqrt{3} + 1}{3 - 1}$

$= \frac{4 - 2 \sqrt{3}}{2}$

$= 2 - \sqrt{3}$

$= 0.2679$

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