How do you solve $tan x csc x - 2 tan x = 0$ $tanxcscx-2tanx=0$ ?

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How do you solve $tan x csc x - 2 tan x = 0$ $tanxcscx-2tanx=0$ ?

1 Answer

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Answer 1 · 2016-08-24T04:39:43

$0, \frac{π}{3}, π, \frac{5 π}{3}, 2 π$ $0, pi/3, pi, (5pi)/3, 2pi$

Explanation:

Trig table of special arcs, and unit circle -->
tan x.csc x - 2tan x = 0
tan x(csc x - 2) = 0
One of the 2 factors should be 0 -->
a. tan x = 0 -->
arc x = 0, and $x = π, and x = 2 π$ $x = pi, and x = 2pi$
b. $csc x = \frac{1}{cos x} = 2$ $csc x = 1/(cos x) = 2$
$cos x = \frac{1}{2}$ $cos x = 1/2$ -->
Arc $x = \pm \frac{π}{3}$ $x = +- pi/3$
Note: arc $- \frac{π}{3}$ $-pi/3$ --> arc $\frac{5 π}{3}$ $(5pi)/3$ (co-terminal)
Answers for $(0, 2 π)$ $(0, 2pi)$ :
$0, \frac{π}{3}, π, \frac{5 π}{3}, and 2 π$ $0, pi/3, pi, (5pi)/3, and 2pi$

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How do you solve $tan x csc x - 2 tan x = 0$ $tanxcscx-2tanx=0$ ?

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How do you solve tanxcscx-2tanx=0tanxcscx−2tanx=0tanxcscx-2tanx=0?

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How do you solve $tan x csc x - 2 tan x = 0$ $tanxcscx-2tanx=0$ ?