Solve: √3 cos θ + sin θ = √2

√3 cos θ + sin θ = √2

Divide the equation by 2 to get

(√3/2) cosθ + (1/2) sinθ = 1/√2 or cos(π/6) cosθ + sin(π/6) sinθ = cos(π/4)

or cos(π/6 − θ) = cos(π/4) or cos(θ − π/6) = cos(π/4)

Thus, the solution are given by i.e., θ = 2mπ ± π/4 + π/6 

Hence, the solution are 

θ = 2mπ + π/4 + π/6 and θ = 2mπ - π/4 + π/6, i.e.,  θ=  2mπ + 5π/12 and θ = 2mπ − π/12