Question

Giải các phương trình sau:

a) \(\sqrt 3 \tan 2x =  - 1\);                              b) \(\tan 3x + \tan 5x = 0\)’

Answer 1

a) \(\sqrt 3 \tan 2x =  - 1\;\; \Leftrightarrow \tan 2x =  - \frac{1}{{\sqrt 3 }}\;\;\; \Leftrightarrow \tan 2x = \tan  - \frac{\pi }{6}\; \Leftrightarrow 2x =  - \frac{\pi }{6} + k\pi \)

\(\;\; \Leftrightarrow x =  - \frac{\pi }{{12}} + \frac{{k\pi }}{2}\;\left( {k \in \mathbb{Z}} \right)\)

b) \(\tan 3x + \tan 5x = 0\;\; \Leftrightarrow \tan 3x = \tan \left( { - 5x} \right) \Leftrightarrow 3x =  - 5x + k\pi \;\; \Leftrightarrow 8x = k\pi \;\; \Leftrightarrow x = \frac{{k\pi }}{8}\;\left( {k \in \mathbb{Z}} \right)\)