Giải phương trình sin 2x + cos ( 6x+pi/3 ) =0

Trả lời

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

$\iff \sin 2x=-\cos \left(6x+\frac{\pi }{3}\right)=\sin \left(6x+\frac{\pi }{3}-\frac{\pi }{2}\right)$

$\iff \sin 2x=\sin \left(6x-\frac{\pi }{6}\right)$

$\iff \left[\begin{array}{l}2x=6x-\frac{\pi }{6}+k2\pi \\ 2x=\pi -6x+\frac{\pi }{6}+k2\pi \end{array}\right.$

$\iff \left[\begin{array}{l}-4x=-\frac{\pi }{6}+k2\pi \\ 8x=\frac{7\pi }{6}+k2\pi \end{array}\right.$

$\iff \left[\begin{array}{l}x=\frac{\pi }{24}+k\frac{\pi }{2}\\ x=\frac{7\pi }{32}+k\frac{\pi }{4}\end{array}\right.$