Question

Answer 1

\(cot\left(x-\dfrac{\pi}{4}\right)=\sqrt{3}\)

\(\Leftrightarrow cot\left(x-\dfrac{\pi}{4}\right)=cot\dfrac{\pi}{6}\)

\(\Leftrightarrow x-\dfrac{\pi}{4}=\dfrac{\pi}{6}+k\pi\)

\(\Leftrightarrow x=\dfrac{5\pi}{12}+k\pi\)

Ta có \(\dfrac{\pi}{2}\le\dfrac{5\pi}{12}+k\pi\le\dfrac{5\pi}{2}\Leftrightarrow\dfrac{1}{12}\le k\le\dfrac{25}{12}\)

Mà \(k\in Z\Rightarrow k\in\left\{1;2\right\}\)

Với \(k=1\Rightarrow x=\dfrac{17\pi}{12}\)

Với \(k=2\Rightarrow x=\dfrac{29\pi}{12}\)