Question

Trên khoảng (\(\dfrac{\pi}{2};2\pi\)) , phương trình \(cos\left(\dfrac{\pi}{6}-2x\right)=sinx\) có bao nhiêu nghiệm

Answer 1

\(cos\left(\dfrac{\pi}{6}-2x\right)=cos\left(\dfrac{\pi}{2}-x\right)\)

\(\Rightarrow\left[{}\begin{matrix}\dfrac{\pi}{6}-2x=\dfrac{\pi}{2}-x+k2\pi\\\dfrac{\pi}{6}-2x=x-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{3}+k2\pi\\x=\dfrac{2\pi}{9}+\dfrac{k2\pi}{3}\end{matrix}\right.\)

\(\Rightarrow x=\left\{\dfrac{8\pi}{9};\dfrac{14\pi}{9};\dfrac{5\pi}{3}\right\}\) có 3 nghiệm