Question

a. sin3x-cos3x-\(\sqrt{2}\)sin\(\left(5x-\dfrac{\pi}{3}\right)\)=0

Answer 1

Đề là \(sin\left(5-\dfrac{\pi}{3}\right)\) hay \(sin\left(5x-\dfrac{\pi}{3}\right)\) nhỉ?

Answer 2

\(sin3x-cos3x=\sqrt{2}sin\left(5x-\dfrac{\pi}{3}\right)\)

\(\Leftrightarrow\sqrt{2}sin\left(3x-\dfrac{\pi}{4}\right)=\sqrt{2}sin\left(5x-\dfrac{\pi}{3}\right)\)

\(\Leftrightarrow sin\left(5x-\dfrac{\pi}{3}\right)=sin\left(3x-\dfrac{\pi}{4}\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}5x-\dfrac{\pi}{3}=3x-\dfrac{\pi}{4}+k2\pi\\5x-\dfrac{\pi}{3}=\dfrac{5\pi}{4}-3x+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{24}+k\pi\\x=\dfrac{19\pi}{96}+\dfrac{k\pi}{4}\end{matrix}\right.\)