a)tan (2x+1)*tan (3x-1)=1
\(\Rightarrow\frac{sin\left(2x+1\right)}{cos\left(2x+1\right)}\cdot\frac{sin\left(3x-1\right)}{cos\left(2x-1\right)}=1\)
\(\Rightarrow cos5xcos\left(2-x\right)-cos5x=cos5x+cos\left(2-x\right)\)
\(\Rightarrow2cos5x=0\)
\(\Rightarrow x=\frac{\pi}{10}+\frac{k\pi}{5}\)
b)Đk:\(cosx\ne0,cos\left(x+\frac{\pi}{4}\right)\)
\(pt\Leftrightarrow tanx+\frac{1+tanx}{1-tanx}=1\)
\(\Leftrightarrow tanx\left(1-tanx\right)+1+tanx=1-tanx\)
\(\Leftrightarrow tanx\cdot\left(1-tanx\right)+2tanx=0\)
\(\Leftrightarrow tanx\left(1-tanx+2\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}tanx=0\\tanx=3\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=k\pi\\x=a+k\pi\left(a=arctan3\right)\end{array}\right.\)
