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