sec x + tan x = 1

Question

I am confused please help

Answer 1

I'm guessing this is an equation you have to solve, right?

 

sec x + tan x = 1

sec x = 1 - tan x

sec² x = (1 - tan x)²                 (square both sides)

sec² x = 1 - 2 tan x + tan² x

1 + tan² x = 1 + tan² x - 2 tax x     (by the Pythagorean identity, 1 + tan² x = sec² x

0 = -2 tan x                                   (subtract 1 + tan² x from both sides)

0 = tan x                                       (divide both sides by -2)

x = Nπ, where N is any integer