Bài tập 1.16 trang 24 SBT Toán 11

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 HỌC247