How do you solve ?

(1-cos8x)/(1+tgx) = 0

Correct answer is x=(kπ)/2 or x=π/4 +kπ

1 Answer
Jun 24, 2018

x = (kpi)/4,
except the 2 values: x = (-pi/4), and x = (3pi)/4

Explanation:

(1 - cos 8x)/(1 + tan x) = 0
(1 - cos 8x) = 0 (1)
Condition tan x != -1 , or x != - pi/4, and x != +(3pi)/4.
Solve equation (1):
cos 8x = 1
Unit circle gives:
8x = 2kpi -->
x = (kpi)/4
(except when x = - pi/4 and x = (3pi)/4)
Specifically,
When k = -1, x = -pi/4 (rejected)
When k = 3 --> x = (3pi)/4 (rejected)
When k = 7 --> x = (7pi)/4 = - pi/4 (rejected)