Tan x+secx=2cosx ?

#tan x+secx=2cosx# ?

1 Answer
Jan 30, 2018

Solve
#tan x + sec x = 2cos x#
#sin x/(cos x) + 1/(cos x) = 2cos x#
#sin x + 1 = 2cos^2 x#
#sin x + 1 = 2 - 2sin^2 x#
#2sin^2 x + sin x - 1 = 0#
Solve the above quadratic equation for sin x.
Since a - b + c = 0, use shortcut. The 2 real roots are:
sin x = -1 and #sin x = - c/a = 1/2#
a. sin x = - 1. Unit circle gives -->
#x = (3pi)/2 + 2kpi#
b. #sin x = 1/2#
Trig table and unit circle give 2 solutions:
#x = pi/6 + 2kpi#
#x = (5pi)/6 + 2kpi#