Question

How do you solve `tan x + sec x = 1`?

Answer 1

`tanx+secx=1`

`tanx=sinx/cosx` and `secx=1/cosx`

`sinx/cosx+1/cosx=1`

`(sinx+1)/cosx=1`

`sinx+1=cosx`

`1=cosx-sinx`

This is only possible if the cosine of x is 1 and the sine is 0. Therefore, the solution set is `{...-4pi, -2pi, 0, 2pi, 4pi,...}`