Question

Giúp em câu 1 của bài 2 với ạ. Em cảm ơn 🙏🙏🙏🙏🙏

Answer 1

\(2cos^2\left(x+\dfrac{\pi}{3}\right)+sin2x=1\)

\(\Leftrightarrow2cos^2\left(x+\dfrac{\pi}{3}\right)-1=-sin2x\)

\(\Leftrightarrow cos\left(2x+\dfrac{2\pi}{3}\right)=-sin2x=cos\left(\dfrac{\pi}{2}+2x\right)\)

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

\(\Rightarrow x=-\dfrac{7\pi}{24}+\dfrac{k\pi}{2}\)