\(sin\left(2x+\dfrac{3\pi}{4}\right)+cosx=0\)
\(\Leftrightarrow cos\left(-\dfrac{\pi}{4}-2x\right)+cosx=0\)
\(\Leftrightarrow cos\left(\dfrac{\pi}{4}+2x\right)+cosx=0\)
\(\Leftrightarrow2cos\left(\dfrac{\pi}{8}+\dfrac{3x}{2}\right).cos\left(\dfrac{\pi}{8}+\dfrac{x}{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos\left(\dfrac{\pi}{8}+\dfrac{3x}{2}\right)=0\\cos\left(\dfrac{\pi}{8}+\dfrac{x}{2}\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{\pi}{8}+\dfrac{3x}{2}=\dfrac{\pi}{2}+k\pi\\\dfrac{\pi}{8}+\dfrac{x}{2}=\dfrac{\pi}{2}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+\dfrac{k2\pi}{3}\\x=\dfrac{3\pi}{4}+k\pi\end{matrix}\right.\)
\(\Rightarrow x=\dfrac{\pi}{4};x=\dfrac{3\pi}{4}\)
.Nhưng khoảng từ pi/2 đến -pi/4 thì vẫn bao gồm đáp án A mà sao mình lại chọn ạ
