How do you solve #tan x + tan 2x +tan3x=0#?
1 Answer
Explanation:
f(x) = tan x + tan 2x + tan 3x = 0
First, apply trig identity:
Put tan 3x in common factor:
Either factor must be zero.
a. tan 3x - 0 -->
b. (1/(1 - tan x.tan 2x) + 1) = 0
1 + (1 - tan x.tan 2x) = 0
2 - tan x.tan 2x = 0
tan x.tan 2x = 2
Calculator gives:
Check by calculator.
x = 60 -->
tan 60 + tan 120 + tan 180 =
x = 35.26 --> tan x = 0.71 --> tan 2x = 2.83 --> tan 3x = - 3.54
tan x + tan 2x + tan 3x = 0.71 + 2.83 - 3.54 = 0. Proved