Question

\(\text{sin (\frac{\Pi}{6} + 3x) + sin (\frac{\Pi}{3} + x) + sin x = cos 5x.}\)

Answer 1

Đề bạn này ghi toàn lỗi dịch mệt quá

\(\Leftrightarrow sin\left(\frac{\pi}{6}+3x\right)+sin\left(\frac{\pi}{3}+x\right)+cos\left(\frac{\pi}{2}-x\right)-cos5x=0\)

\(\Leftrightarrow2sin\left(2x+\frac{\pi}{4}\right)cos\left(x-\frac{\pi}{12}\right)+2sin\left(2x+\frac{\pi}{4}\right)sin\left(3x-\frac{\pi}{4}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sin\left(2x+\frac{\pi}{4}\right)=0\\cos\left(x-\frac{\pi}{12}\right)=-sin\left(3x-\frac{\pi}{4}\right)=cos\left(3x+\frac{\pi}{4}\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+\frac{\pi}{4}=k\pi\\x-\frac{\pi}{12}=3x+\frac{\pi}{4}+k2\pi\\x-\frac{\pi}{12}=-3x-\frac{\pi}{4}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow...\)