Giải phương trình lượng giác sau: a) tan(x − pi/6) = −căn bậc hai 3

Lời giải

a)

\[\tan \left( {x - \frac{\pi }{6}} \right) = \tan \left( { - \frac{\pi }{3}} \right) \Leftrightarrow x - \frac{\pi }{6} =  - \frac{\pi }{3} + k\pi .\]

b)

\(\sin (\frac{{2\pi }}{5} + 2x) = co{\mathop{\rm s}\nolimits} x \Leftrightarrow \sin (\frac{{2\pi }}{5} + 2x) = \sin \left( {\frac{\pi }{2} - x} \right) \Leftrightarrow \left[ \begin{array}{l}\frac{{2\pi }}{5} + 2x = \frac{\pi }{2} - x + k2\pi \\\frac{{2\pi }}{5} + 2x = \pi  - \left( {\frac{\pi }{2} - x} \right) + k2\pi \end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l}3x = \frac{\pi }{{10}} + k2\pi \\x = \frac{\pi }{{10}} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{{30}} + \frac{{k2\pi }}{3}\\x = \frac{\pi }{{10}} + k2\pi \end{array} \right.(k \in \mathbb{Z})\)