Question

 

Giải pt

Answer 1

5.

\(\sqrt{3}cosx-sinx=\sqrt{2}\)

\(\Leftrightarrow\dfrac{\sqrt{3}}{2}cosx-\dfrac{1}{2}sinx=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow cos\left(x+\dfrac{\pi}{6}\right)=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow x+\dfrac{\pi}{6}=\pm\dfrac{\pi}{4}+k2\pi\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{12}+k2\pi\\x=-\dfrac{5\pi}{12}+k2\pi\end{matrix}\right.\)

Answer 2

6.

ĐK: \(x\ne\dfrac{k\pi}{2}\)

\(-\sqrt{3}cot2x-3=0\)

\(\Leftrightarrow cot2x=-\sqrt{3}\)

\(\Leftrightarrow2x=-\dfrac{\pi}{6}+k\pi\)

\(\Leftrightarrow x=-\dfrac{\pi}{12}+\dfrac{k\pi}{2}\)