Question

Find all solutions in the interval [0, 2π). tan x + sec x = 1

Answer 1

Use the identity 
sec^2x = 1 + tan^2 x
- so sec x = sqrt(1 + tan^2 x) then:-
tan x + sqrt( 1 + tan^2 x) = 1
sqrt ( 1 + tan^2 x) = 1 - tan x
1 + tan^2 x  = 1 + tan^2x - 2 tan x
0 = -2 tanx 

tan x = 0 

x =  0, π 
π is an extraneous root because sec 180 = -1 
So the answer  is 0 degrees