Question

Solve cosx+sqrt3sinx=2

Answer 1

Use substitution: sinx = sqrt(1-cos^2)

$2- cos x = \sqrt{3} \sqrt{1-cos^2 x} \\ \\ (2-cos x)^2 = 3(1-cos^2 x)$

At this point, use another substitution, u = cos x
Then solve the quadratic for u

$(2-u)^2 = 3(1-u^2) \\ \\ 4u^2 -4u+1 = 0 \\ \\ u = \frac{1}{2}$

Sub back in cos x

$cos x = \frac{1}{2} \\ \\ x = \frac{\pi}{3}$