Question

Найдите ctgX если
$\frac{ 5\sin(x) - 2 \cos(x) }{3 \cos(x) + 2 \sin(x) } = 3$
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Answer 1

Найти: $ctg x = \frac{\cos x}{\sin x}$.

$\frac{5\sin x - 2\cos x}{3\cos x + 2\sin x} = 3\\5\sin x - 2\cos x = 3(3\cos x + 2\sin x)\\5\sin x - 2\cos x = 9\cos x + 6\sin x\\5\sin x - 6\sin x = 9\cos x + 2\cos x\\-\sin x = 11\cos x\\-\frac{\sin x}{\cos x} = 11\\\frac{\sin x}{\cos x} = -11\\\frac{\cos x}{\sin x} = -\frac{1}{11}$

Ответ: $-\frac{1}{11}$.