{ ((y sin x+cos x = 2)),((4sin x−2y cos x = y)) :} tan x =?


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Question Number 195263 by dimentri last updated on 28/Jul/23

${\begin{cases} y \sin x + \cos x = 2 \\ 4 \sin x - 2 y \cos x = y \end{cases}$ $\tan x = ?$
	Answered by cortano12 last updated on 28/Jul/23

	${\begin{cases} \underset{―}{\underset{⏟}{}} \end{cases}$
	Answered by Frix last updated on 28/Jul/23
	${ ((y=((2−cos x)/(sin x)))),((y=((4sin x)/(1+2cos x)))) :} ((2−cos x)/(sin x))=((4sin x)/(1+2cos x)) cos^2 x +(3/2)cos x −1=0 cos x =(1/2) [∨cos x =−2] tan x =±((√(1−cos^2 x))/(cos x))=±(√3)$
	${\begin{cases} y = \frac{2 - \cos x}{\sin x} \\ y = \frac{4 \sin x}{1 + 2 \cos x} \end{cases}$ $\frac{2 - \cos x}{\sin x} = \frac{4 \sin x}{1 + 2 \cos x}$ $\cos^{2} x + \frac{3}{2} \cos x - 1 = 0$ $\cos x = \frac{1}{2} [\lor \cos x = - 2]$ $\tan x = \pm \frac{\sqrt{1 - \cos^{2} x}}{\cos x} = \pm \sqrt{3}$
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