Question

4cos^4-9cos2x-1=0

Тригонометрия

Answer 1

Ответ:

Пошаговое объяснение:

$4cos^{4}x - 9cos2x - 1 =0\\cos^{4}x = cos^{2}x * cos^{2}x = \frac{1 + cos2x}{2} * \frac{1 + cos2x}{2} \\\\(1 + cos2x)^{2} +9cos2x - 1 = 0\\cos2x^{2} +11cos2x = 0\\cos2x(cos2x + 11) = 0\\cos2x = 0\\\left \[] {{x =\frac{\pi }{4} + 2\pi k } \atop {x=-\frac{\pi }{4} +2\pi k}} \right$

б) x = 2π - $\frac{\pi }{4}$ x= 2π + $\frac{\pi }{4}$