Question

Решите уравнение с объяснением пж!

cosx(2x+2pi/3)= корень из 2/2
pi - число пи

Answer 1

Ответ: x=-5p/24+pn,   x=-11p/4+pn,   n    E    Z

Объяснение:

наверно  cos(2x+2p/3)=V2 /2  (V-корень)

аргумент (2x+2p/3)= arc cos V2 /2  +2pn,  u  2x+2p/3= -arccos V2/2 +2pn

2x+2p/3 =p/4 +2pn,  2x=-2p/3+p/4 +2pn,  2x= -5p/12 +2pn,  x=-5p/24 +pn,

2x+2p/3= -p/4+2pn,  2x=-2p/3-p/4+2pn,   2x= -11p/12+2pn,   x=-11p/24 +pn,

n     E     Z

Answer 2

$Cos(2x+\frac{2\pi }{3} )=\frac{\sqrt{2} }{2}\\\\\left[\begin{array}{ccc}2x+\frac{2\pi }{3}=arcCos\frac{\sqrt{2} }{2}+2\pi n,n\in Z \\2x+\frac{2\pi }{3}=-arcCos\frac{\sqrt{2} }{2}+2\pi n,n\in Z\end{array}\right\\\\\\\left[\begin{array}{ccc}2x+\frac{2\pi }{3}=\frac{\pi }{4} +2\pi n,n\in Z\\2x+\frac{2\pi }{3}=-\frac{\pi }{4} +2\pi n,n\in Z\end{array}\right$

$\left[\begin{array}{ccc}2x=\frac{\pi }{4}-\frac{2\pi }{3} +2\pi n,n\in Z\\2x=-\frac{\pi }{4}-\frac{2\pi }{3} +2\pi n,n\in Z\end{array}\right \\\\\\\left[\begin{array}{ccc}2x=-\frac{5\pi }{12}+2\pi n,n\in Z \\2x=-\frac{11\pi }{12}+2\pi n,n\n Z \end{array}\right\\\\\\\left[\begin{array}{ccc}x=-\frac{5\pi }{24}+\pi n,n\in Z \\x=-\frac{11\pi }{24}+\pi n,n\in Z \end{array}\right$