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madam [21]
3 years ago
13

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

Mathematics
1 answer:
svp [43]3 years ago
6 0
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
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