a. \(\tan 3x = \tan {{3\pi } \over 5} \Leftrightarrow 3x = {{3\pi } \over 5} + k\pi \Leftrightarrow x = {\pi \over 5} + k{\pi \over 3}\)
b. \(\tan(x – 15^0) = 5⇔ x = α + 15^0+ k180^0\),
trong đó \(\tan α = 5\) (chẳng hạn, có thể chọn \(α ≈ 78^041’24”\) nhờ dùng máy tính bỏ túi)
c.
\(\eqalign{
& \tan \left( {2x - 1} \right) = \sqrt 3 \Leftrightarrow \tan \left( {2x - 1} \right) = \tan {\pi \over 3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow 2x - 1 = {\pi \over 3} + k\pi \Leftrightarrow x = {\pi \over 6} + {1 \over 2} + k{\pi \over 2};k \in\mathbb Z \cr} \)
d.
\(\cot 2x = \cot \left( { - {1 \over 3}} \right) \Leftrightarrow 2x = - {1 \over 3} + k\pi \Leftrightarrow x = - {1 \over 6} + k{\pi \over 2}\)
e.
\(\eqalign{
& \cot \left( {{x \over 4} + 20^\circ } \right) = - \sqrt 3 \Leftrightarrow \cot \left( {{x \over 4} + 20^\circ } \right) = \cot \left( { - 30^\circ } \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow {x \over 4} + 20^\circ = - 30^\circ + k180^\circ \Leftrightarrow x = - 200^\circ + k720^\circ \cr} \)
f.
\(\cot 3x = \tan {{2\pi } \over 5} \Leftrightarrow \cot 3x = \cot \left( {{\pi \over 2} - {{2\pi } \over 5}} \right) \Leftrightarrow 3x = {\pi \over {10}} + k\pi \Leftrightarrow x = {\pi \over {30}} + k.{\pi \over 3}\)
