Question

Cho cos a= \(\frac{1}{3}\) (\(\frac{3\pi}{2}\) < a < \(2\pi\))

Tính tan (a - \(\frac{\pi}{3}\))

Answer 1

\(\frac{3\pi}{2}< a< 2\pi\Rightarrow sina< 0\) \(\Rightarrow sina=-\sqrt{1-cos^2a}=\frac{-2\sqrt{2}}{3}\)

\(tan\left(a-\frac{\pi}{3}\right)=\frac{sin\left(a-\frac{\pi}{3}\right)}{cos\left(a-\frac{\pi}{3}\right)}=\frac{sina.cos\frac{\pi}{3}-cosa.sin\frac{\pi}{3}}{cosa.cos\frac{\pi}{3}+sina.sin\frac{\pi}{3}}=\frac{\frac{-2\sqrt{2}}{3}.\frac{1}{2}-\frac{1}{3}.\frac{\sqrt{3}}{2}}{\frac{1}{3}.\frac{1}{2}-\frac{2\sqrt{2}}{3}.\frac{\sqrt{3}}{2}}=\frac{9\sqrt{3}+8\sqrt{2}}{23}\)