Question

giải các phương trình sau : a) \(\tan3x=\tan\frac{3\pi}{5}\)   ;  b) \(\tan\left(x-15^o\right)=5\)   ;   c) \(\tan\left(2x-1\right)=\sqrt{3}\)   ;   d) \(\cot2x=\cot\left(-\frac{1}{3}\right)\)   ;   e) \(\cot\left(\frac{x}{4}+20^o\right)=-\sqrt{3}\)   ;   f) \(\cot3x=\tan\frac{2\pi}{5}\)

Answer 1

b)đề là \(tan\left(x-15^0\right)=\frac{\sqrt{3}}{3}\)

Vì \(\frac{\sqrt{3}}{3}=tan30^0\) nên

\(\Leftrightarrow tan\left(x-15^0\right)=tan30^0\)

\(\Leftrightarrow x-15^0=30^0+k180^0\)

\(\Leftrightarrow x=45^0+k180^0\left(k\in Z\right)\)

Answer 2

Đk:\(sin3x\ne0\) và \(cos\frac{2\pi}{5}\ne0\)

\(\Leftrightarrow\frac{cos3x}{sin3x}-\frac{sin\frac{2\pi}{5}}{cos\frac{2\pi}{5}}=0\)

\(\Leftrightarrow cos3x\cdot cos\frac{2\pi}{5}-sin\frac{2\pi}{5}\cdot sin3x=0\)

\(\Leftrightarrow cos\left(3x+\frac{2\pi}{5}\right)=0\)

\(\Leftrightarrow3x+\frac{2\pi}{5}=\frac{\pi}{2}+k\pi\)

\(\Leftrightarrow x=\frac{\pi}{30}+\frac{k\pi}{3}\)

Answer 3

cái bài dưới là phần f)cot3x=tan 2pi/5