Решим уравнение:
[tex]2 \cos(2x - \frac{\pi}{4} ) = \sqrt{3} \\ [/tex]
Разделим обе части на 2:
[tex] \cos(2x - \frac{\pi}{4} ) = \frac{ \sqrt{3} }{2} \\ [/tex]
Решим простейшее тригонометрическое уравнение:
[tex]2x - \frac{\pi}{4} = ± \arccos( \frac{ \sqrt{3} }{2} ) + 2n\pi,n∈Z \\ [/tex]
[tex]2x - \frac{\pi}{4} = ± \frac{\pi}{6} + 2\pi n,n∈Z \\ [/tex]
[tex]x - \frac{\pi}{8} = ± \frac{\pi}{12} + n\pi,n∈Z \\ [/tex]
Тогда:
[tex]x = \frac{\pi}{12} + \frac{\pi}{8} + n\pi = \frac{5}{24} \pi + n\pi,n∈Z \\ [/tex]
[tex]x = - \frac{\pi}{12} + \frac{\pi}{8} + n\pi = \frac{1}{24} \pi + n\pi,n∈Z \\ [/tex]
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Answers & Comments
Решим уравнение:
[tex]2 \cos(2x - \frac{\pi}{4} ) = \sqrt{3} \\ [/tex]
Разделим обе части на 2:
[tex] \cos(2x - \frac{\pi}{4} ) = \frac{ \sqrt{3} }{2} \\ [/tex]
Решим простейшее тригонометрическое уравнение:
[tex]2x - \frac{\pi}{4} = ± \arccos( \frac{ \sqrt{3} }{2} ) + 2n\pi,n∈Z \\ [/tex]
[tex]2x - \frac{\pi}{4} = ± \frac{\pi}{6} + 2\pi n,n∈Z \\ [/tex]
Разделим обе части на 2:
[tex]x - \frac{\pi}{8} = ± \frac{\pi}{12} + n\pi,n∈Z \\ [/tex]
Тогда:
[tex]x = \frac{\pi}{12} + \frac{\pi}{8} + n\pi = \frac{5}{24} \pi + n\pi,n∈Z \\ [/tex]
[tex]x = - \frac{\pi}{12} + \frac{\pi}{8} + n\pi = \frac{1}{24} \pi + n\pi,n∈Z \\ [/tex]