Tanx=(2sqrt3/3)sinx What are all solutions?

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Tanx=(2sqrt3/3)sinx What are all solutions?

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Answer 1 · 2015-10-29T17:50:33

Solve $tan x = (\frac{2 \sqrt{3}}{3}) . sin x$ $tan x = ((2sqrt3)/3).sin x$

Ans: $0, π, 2 π, \pm \frac{π}{6}$ $0, pi, 2pi, +- pi/6$

Explanation:

$tan x = (\frac{2 \sqrt{3}}{3}) . sin x$ $tan x = ((2sqrt3)/3).sin x$
$\frac{sin x}{cos x} = (\frac{2 \sqrt{3}}{3}) . sin x$ $(sin x)/(cos x) = ((2sqrt3)/3).sin x$
$sin x = (\frac{2 \sqrt{3}}{3}) . sin x . cos x$ $sin x = ((2sqrt3)/3).sin x.cos x$
$3 sin x - (2 \sqrt{3} cos x . sin x) = 0$ $3sin x - (2sqrt3cos x.sin x) = 0$
$sin x (3 - 2 \sqrt{3} . cos x) = 0$ $sin x (3 - 2sqrt3.cos x) = 0$

a. sin x = 0 --> x = 0; $x = π$ $x = pi$ ; and $x = 2 π$ $x = 2pi$
b. $3 - (2 \sqrt{3}) cos x = 0$ $3 - (2sqrt3)cos x = 0$ --> $(2 \sqrt{3} cos x) = 3$ $(2sqrt3cos x) = 3$
$cos x = \frac{3}{2 \sqrt{3}} = \frac{\sqrt{3}}{2}$ $cos x = 3/(2sqrt3) = sqrt3/2$ --> $x = \pm \frac{π}{6}$ $x = +- pi/6$

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Tanx=(2sqrt3/3)sinx What are all solutions?

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