How do you find the general solutions for $tanx = 2sinx$ ?

Question

37666 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-13T02:09:24

$tanx = 2sinx$

$tanx - 2sinx =0$

$sinx/cosx - 2sinx =0$

$sinx(1/cosx -2) =0$

$sinx =0" "$ or $" "1/cosx-2=0$

$sinx =0" "$ or $" "cosx=1/2$

$sinx = 0$ $hArr$ $x=pin$ for $n$ an Integer.

$cosx=1/2$ $hArr$ $x = pi/3 +2pin$ $" or "$ $x = -pi/3 +2pin$

The solutions are:

${: (x = pi n), (x = pi/3 +2pi n), (x = - pi/3 +2pi n):} }$ for $n$ an Integer.

How do you find the general solutions for tanx = 2sinxtanx = 2sinx?