Solve the equation:
tanx + secx =√3
tan x + sec x = √3
= sin x/cos x + 1/cos x
= (sin x + 1)/cos x
⇒ √3 cos x - sin x = 1
Divide both sides by 2:
= (√3/2) cos x - (1/2) sin x = 1/2
= cos π/6 cos x - sin π/6 sin x = 1/2
= cos (x + π/6) = cos π/3
x + π/6 = 2mπ ± π/3
x = 2mπ + π/3 - π/6
x = 2mπ + π/6, 2mπ - π/2
cos θ = cos (2mπ - π/2) = cos π/2 = 0, which is not wanted.
Therefore solution is θ = 2mπ + π/6