Giải các phương trình:
a) tan(2x+45o) = −1
b) \(\cot(x + \frac{\pi }{3}) = \sqrt 3 \)
c) \(\tan \left( {\frac{x}{2} - \frac{\pi }{4}} \right) = \tan \frac{\pi }{8}\)
d) \(\cot (\frac{x}{3} + {20^o}) = - \frac{{\sqrt 3 }}{3}.\)
a) tan(2x+45o) = −1
\(\tan (2x + {45^o}) = \tan ( - {45^o})\)
\( \Leftrightarrow 2x + {45^o} = - {45^o} + k{180^o},k \in Z\)
\( \Leftrightarrow x = - {45^o} + k{90^o},k \in Z\)
b) \(\cot(x + \frac{\pi }{3}) = \sqrt 3 \)
\( \Leftrightarrow \cot (x + \frac{\pi }{3}) = \cot \frac{\pi }{6}\)
\( \Leftrightarrow x + \frac{\pi }{3} = \frac{\pi }{6} + k\pi ,k \in Z\)
\( \Leftrightarrow x = - \frac{\pi }{6} + k\pi ,k \in Z\)
c) \(\tan (\frac{x}{2} - \frac{\pi }{4}) = \tan \frac{\pi }{8}\)
\( \Leftrightarrow \frac{x}{2} - \frac{\pi }{4} = \frac{\pi }{8} + k\pi ,k \in Z\)
\( \Leftrightarrow x = \frac{{3\pi }}{4} + k2\pi ,k \in Z\)
d) \(\cot (\frac{x}{3} + {20^o}) = - \frac{{\sqrt 3 }}{3}.\)
\( \Leftrightarrow \cot (\frac{\pi }{3} + {20^o}) = \cot ( - {60^o})\)
\( \Leftrightarrow \frac{x }{3} + {20^o} = - {60^o} + k{180^o},k \in Z\)
\( \Leftrightarrow x = - {240^o} + k{540^o},k \in Z\)
-- Mod Toán 11