Question

Cos(3x-П/6)=Cos(x+П/4)

Answer 1

$cos(3x-\frac{\pi}6)=cos(x+\frac{\pi}4)\\cos(3x-\frac{\pi}6)-cos(x+\frac{\pi}4)=0$

Воспользуемся формулой:  $cosa-cosb=-2*sin(\frac{a+b}2)*sin(\frac{a-b}2)$

$-2*sin(\frac{3x-\frac{\pi}6+x+\frac{\pi}4}2)*sin(\frac{3x-\frac{\pi}6-x-\frac{\pi}4}2)=0\\\\sin(\frac{4x-\frac{2\pi}{12}+\frac{3\pi}{12}}2)*sin(\frac{2x-\frac{2\pi}{12}-\frac{3\pi}{12}}2)=0\\\\sin(\frac{4x+\frac{\pi}{12}}2)*sin(\frac{2x-\frac{5\pi}{12}}2)=0\\\\ \left[\begin{array}{ccc}sin(\frac{4x+\frac{\pi}{12}}2)=0\\\\sin(\frac{2x-\frac{5\pi}{12}}2)=0\end{array}\right=\ \textgreater \ \left[\begin{array}{ccc}\frac{4x+\frac{\pi}{12}}2=\pi n;n\in Z\\\\\frac{2x-\frac{5\pi}{12}}2=\pi n;n\in Z\end{array}\right=\ \textgreater$

$=\ \textgreater \ \left[\begin{array}{ccc}4x+\frac{\pi}{12}=2\pi n;n\in Z\\\\2x-\frac{5\pi}{12}=2\pi n;n\in Z\end{array}\right=\ \textgreater \ \left[\begin{array}{ccc}4x=-\frac{\pi}{12}+2\pi n;n\in Z\\\\2x=\frac{5\pi}{12}+2\pi n;n\in Z\end{array}\right=\ \textgreater$

$=\ \textgreater \ \left[\begin{array}{ccc}x=-\frac{\pi}{48}+\frac{\pi n}2;n\in Z\\\\x=\frac{5\pi}{24}+\frac{\pi n}2;n\in Z\end{array}\right$