Question

2sinx+tanx=0 solve this equation

Answer 1

$2 \sin(x) + \tan(x) = 0$
$2 \sin(x) + \frac{ \sin(x) }{ \cos(x) } = 0$
$\sin(x) (2 + \frac{1}{ \cos(x) } ) = 0$
There are two possible cases now.
First,
$\sin(x) = 0$
Second,
$\cos(x) = - \frac{ 1}{2}$
Solving the first case gives
$x = k\pi$
Where k is an integer.

For the second case, there are another two cases since
$\cos(x) = \cos(2\pi - x)$

Solving both cases separately gives
$x = \frac{2\pi}{3} + 2k\pi$
and
$x = \frac{4\pi}{3} + 2k\pi$
Where k is an integer.

These are the solutions of the equation. Thank You.