How do you derive the general solution for the trigonometric equation sin(theta) + sqrt(3)cos(theta) = 1?

To derive the general solution for the equation sin(θ) + √3 cos(θ) = 1, we can use the method of expressing the equation in the form of a single trigonometric function. Start by rewriting the equation in the form R sin(θ + φ) = 1, where R = √(1^2 + (√3)^2) = 2 and tan(φ) = √3. Thus, sin(θ + π/3) = 1/2. The general solution is θ + π/3 = nπ + (-1)^n π/6, where n is an integer. Solving for θ gives θ = nπ – π/6 + (-1)^n π/6.

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