Question

Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`

Answer 1

Divide the given equation by 2 to get

`sqrt(3)/2 cos theta + 1/2 sin theta = 1/sqrt(2)`

or `cos  pi/6 cos theta + sin  pi/6 sin theta = cos  pi/4`

or `cos(pi/6 - theta) = cos  pi/4` or `cos(theta - pi/6) = cos  pi/4` 

Thus, the solution is given by, i.e., θ = `2 m pi +- pi/4 + pi/6`

Hence, the solution is

θ = `2 m pi + pi/4 + pi/6` and `2 m pi - pi/4 + pi/6,` i.e., `theta = 2 m pi + (5pi)/12` and `theta = 2 m pi - pi / 12`