Question

If tan θ + sec θ = `sqrt(3)`, find the general value of θ.

Answer 1

tan θ + sec θ = `sqrt(3)`

∴ `sinθ/cosθ + 1/cosθ = sqrt(3)`

∴ 1 + sin θ = `sqrt(3) cos θ`

∴ `sqrt(3) cos θ - sin θ` = 1

∴ `sqrt(3)/2 cos θ - 1/2 sin θ = 1/2`

∴ `cos  π/6 cos θ - sin  π/6 sin θ = cos  π/3`

∴ `cos(θ + π/6) = cos  π/3`

∴ `θ + π/6 = 2nπ ± π/3`

∴ θ = `2nπ ± π/3 - π/6`

∴ θ = `2nπ + π/3 - π/6`

or θ = `2nπ - π/3 - π/6`

∴ θ = `2nπ + π/6`

or θ = `2nπ - π/2`