a. ĐKXĐ: ...
\(cot\left(2\pi-\frac{\pi}{3}-3x\right)=tan\left(2x+\frac{\pi}{3}\right)\)
\(\Leftrightarrow cot\left(-3x-\frac{\pi}{3}\right)=tan\left(2x+\frac{\pi}{3}\right)\)
\(\Leftrightarrow tan\left(3x+\frac{5\pi}{6}\right)=tan\left(2x+\frac{\pi}{3}\right)\)
\(\Leftrightarrow3x+\frac{5\pi}{6}=2x+\frac{\pi}{3}+k\pi\)
\(\Leftrightarrow...\)
b. ĐKXĐ: \(x\ne\frac{k\pi}{2}\)
\(\frac{cosx.cos2x}{sinx.sin2x}=-1\)
\(\Leftrightarrow cosx.cos2x=-sinx.sin2x\)
\(\Leftrightarrow cosx.cos2x+sinx.sin2x=0\)
\(\Leftrightarrow cosx=0\)
\(\Leftrightarrow x=\frac{\pi}{2}+k\pi\) (ktm)
Vậy pt vô nghiệm
c. ĐKXĐ: ...
\(tanx=\frac{3}{tanx}\)
\(\Leftrightarrow tan^2x=3\)
\(\Rightarrow tanx=\pm\sqrt{3}\)
\(\Rightarrow x=\pm\frac{\pi}{3}+k\pi\)
d.
\(2sin^2x+1-2sin^2x=2\)
\(\Leftrightarrow1=2\) (vô lý)
Vậy pt vô nghiệm
