Question

Giải phương trình sau

sin\(\left(3x+\frac{2\pi}{3}\right)\)=cos\(\left(x-\frac{9\pi}{4}\right)\)

Answer 1

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

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

\(\Leftrightarrow sin\left(3x+\frac{2\pi}{3}\right)=sin\left(\frac{3\pi}{4}-x\right)\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{48}+\frac{k\pi}{4}\\x=-\frac{5\pi}{24}+k\pi\end{matrix}\right.\)

Answer 2

:( idol