Question

Sin (2x + π/3) = cos (π/3-x)

Answer 1

Lời giải:

$\cos (\frac{\pi}{3}-x)=\sin (2x+\frac{\pi}{3})=\cos [\frac{\pi}{2}-(2x+\frac{\pi}{3})]=\cos (\frac{\pi}{6}-2x)$

$\Leftrightarrow \cos (\frac{\pi}{3}-x)-\cos (\frac{\pi}{6}-2x)=0$

$\Leftrightarrow -2\sin (\frac{\pi}{4}-\frac{3}{2}x)\sin (\frac{\pi}{12}+\frac{x}{2})=0$

$\Rightarrow \sin (\frac{\pi}{4}-\frac{3}{2}x)=0$ hoặc $\sin (\frac{\pi}{12}+\frac{x}{2})=0$

$\Rightarrow x=\frac{\pi}{6}-\frac{2}{3}k\pi$ hoặc $x=2k\pi -\frac{\pi}{6}$ với $k$ nguyên.