Question

Answer 1

17. `tan(2x+π/6)=cotx`

`<=> tan(2x+π/6)=tan (π/2-x)`

`<=> 2x+π/6 = π/2 -x+kπ`

`<=> x=π/9 + k π/3 (k \in ZZ)`.

Answer 2

18. `tan xtan3x=0`

\(\Leftrightarrow\left[{}\begin{matrix}tanx=0\\tan3x=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\dfrac{k\pi}{3}\end{matrix}\right.\) `(k \in ZZ)`