Question

find the general solution of 2 sinx + tanx = 0 answer with full explanation
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Answer 1

Step-by-step explanation:

First things first

$tan x \neq\infty\\x \neq { \frac{(2n + 1)\pi}{2} }$

$2 \sin(x) + \frac{ \sin(x) }{ \cos(x) } = 0 \\ \frac{2 \sin(x) \cos(x) + \sin(x) }{ \cos(x) } = 0 \\ \sin(x) (2 \cos(x) + 1) = 0 \\ \sin(x) = 0 \: \: and \: \: \cos(x) = \frac{ - 1}{2} \\ x = n\pi \: \: and \: \: 2n\pi \pm \frac{2\pi}{3}$