Question

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

Answer 1

`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 = pi, and x = 2pi`
b. `csc x = 1/(cos x) = 2`
`cos x = 1/2`-->
Arc `x = +- pi/3`
Note: arc `-pi/3` --> arc `(5pi)/3` (co-terminal)
Answers for `(0, 2pi)`:
`0, pi/3, pi, (5pi)/3, and 2pi`