Tan x + sec x = 1
Solve equation for 0 less than or equal to X less than 2 pi© BrainMass Inc. brainmass.com March 4, 2021, 6:03 pm ad1c9bdddf
sin(x)/cos(x)+ 1/cos(x)= 1 ---> (1+ sin(x))/cos(x)= 1 ---> 1+ sin(x)= cos(x) (Assuming that cos(x) is not zero)
We know that sin(x)= 2sin(x/2)cos(x/2) and cos(x)= 1- 2[sin(x/2)]^2. Therefore:
1+ 2sin(x/2)cos(x/2)= 1- ...
This shows how to solve a trigonometric equation in a given interval.