1.
\(cos^2x-sin^2x=cosx\Leftrightarrow cos2x=cosx\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=x+k2\pi\\2x=-x+k2\pi\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=k2\pi\\x=\frac{k2\pi}{3}\end{matrix}\right.\)
Nghiệm âm lớn nhất là \(x=-\frac{2\pi}{3}\)
2.
ĐKXĐ: ...
\(\Leftrightarrow1+sinx+cosx+\frac{sinx}{cosx}=0\)
\(\Leftrightarrow1+cosx+sinx\left(\frac{cosx+1}{cosx}\right)=0\)
\(\Leftrightarrow\left(1+cosx\right)\left(1+\frac{sinx}{cosx}\right)=0\)
\(\Leftrightarrow\left(1+cosx\right)\left(1+tanx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=-1\\tanx=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\pi+k2\pi\\x=-\frac{\pi}{4}+k\pi\end{matrix}\right.\)
Nghiệm dương bé nhất là \(x=\frac{3\pi}{4}\)
