Question

Cos ( 4x + π/3) = sin ( x + π/5)

Answer 1

Lời giải:

Ta có:

$\cos (4x+\frac{\pi}{3})=\sin (x+\frac{\pi}{5})=\cos [\frac{\pi}{2}-(x+\frac{\pi}{5})]=\cos (\frac{3}{10}\pi-x)$

$\Leftrightarrow \cos (4x+\frac{\pi}{3})-\cos (\frac{3}{10}\pi-x)=0$

$\Leftrightarrow -2\sin (\frac{3}{2}x+\frac{19}{60}\pi)\sin (\frac{5}{2}x-\frac{\pi}{60})=0$

$\Rightarrow \sin (\frac{3}{2}x+\frac{19}{60}\pi)=0$ hoặc $\sin (\frac{5}{2}x-\frac{\pi}{60})=0$

$\Rightarrow x=\frac{2}{3}k\pi-\frac{19}{90}\pi$ hoặc $x=\frac{2}{5}k\pi+\frac{\pi}{150}$ với $k$ nguyên.