Question

cos^2((pi/4) +3x) +5sin(6x) =-4

Answer 1

Ответ:

$x = -\frac{\pi}{12} + \frac{\pi n}{3}$

Пошаговое объяснение:

Применяем формулу двойного угла для косинуса. А затем формулу приведения.

$cos^2(\frac{\pi}{4} +3x) +5sin(6x) =-4 | \cdot 2\\\\2cos^2(\frac{\pi}{4} +3x) + 10sin(6x) =-8 \\\\(2cos^2(\frac{\pi}{4} +3x) - 1) + 1 + 10sin(6x) =-8\\\\cos (2 \cdot (\frac{\pi}{4} +3x)) + 1 + 10sin(6x) = -8\\\\cos (2 \cdot \frac{\pi}{4} +2 \cdot 3x) + 10sin(6x) = -8 - 1\\\\cos (\frac{\pi}{2} + 6x) + 10sin(6x) = -9\\\\cos (\frac{\pi}{2} + 6x) + 10sin(6x) = -9\\\\-sin(6x) + + 10sin(6x) = -9\\\\9 sin(6x) = -9\\\\sin(6x) = -9 : 9\\\\sin(6x) = -1\\\\6x = -\frac{\pi}{2} + 2 \pi n$

$x = -\frac{\pi}{2}:6 + 2 \pi n :6\\\\x = -\frac{\pi}{12} + \frac{\pi n}{3}$

Ответ:  $x = -\frac{\pi}{12} + \frac{\pi n}{3}$

Формула двойного угла: $2cos^{2}(x) - 1 = cos (2x)$

Формула приведения: $cos(90^{0} + x) = - sin (x)$