Simplify:
sec(x) - tan(x) / sec(x) + tan(x)
Show answer & explanation
Correct answer: B
Explanation
(sec x − tan x) / (sec x + tan x)
According to the formula:
sec x = 1 / cos x
tan x = sin x / cos x
(sec x − tan x) / (sec x + tan x)
= (1/cos x − sin x/cos x) / (1/cos x + sin x/cos x)
= ((1 − sin x)/cos x) / ((1 + sin x)/cos x)
= (1 − sin x) / (1 + sin x)