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Ответ:

Решить тригонометрические уравнения .

[tex]\displaystyle \bf a)\ \ cos(\frac{x}{2}-\frac{\pi }{4})=-1\\\\\\\frac{x}{2}-\frac{\pi }{4}=\pi +2\pi n\ \ ,\ \ n\in Z\\\\\\\frac{x}{2}=\frac{\pi }{4}+\pi +2\pi n\ \ ,\ \ n\in Z\\\\\\\frac{x}{2}=\frac{5\pi }{4}+2\pi n\ \ ,\ \ n\in Z\\\\\\x=\frac{5\pi }{2}+\pi +4\pi n\ \ ,\ \ n\in Z\ \ -\ \ \ otvet[/tex]  

[tex]\displaystyle \bf b)\ \ \sqrt3\, tg\, 4x=3\\\\tg4x=\sqrt3\\\\\\4x=\frac{\pi}{3}+\pi n\ \ ,\ \ n\in Z\\\\\\x=\frac{\pi }{12}+\frac{\pi n}{4} \ ,\ \ n\in Z\ \ -\ \ \ otvet[/tex]