\(tan\dfrac{\pi}{6}+tan\dfrac{2\pi}{9}+tan\dfrac{5\pi}{18}+tan\dfrac{\pi}{3}\)\(=\left(tan\dfrac{\pi}{6}+tan\dfrac{\pi}{3}\right)+\left(tan\dfrac{2\pi}{9}+tan\dfrac{5\pi}{18}\right)\) (1)
Áp dụng công thức: \(tanx+tan\left(90^o-x\right)=tanx+cotx=\dfrac{1}{sinx.cosx}\)
Ta được:(1) = \(\dfrac{1}{sin\dfrac{\pi}{6}cos\dfrac{\pi}{6}}+\dfrac{1}{sin\dfrac{2\pi}{9}.cos\dfrac{2\pi}{9}}\)
\(=\dfrac{2}{sin\dfrac{\pi}{3}}+\dfrac{3}{sin\dfrac{4\pi}{9}}\)
Em làm tiếp nhé.