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प्रश्न
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
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उत्तर
Divide each term by 2
`1/2 sin theta + sqrt(3)/2 cos theta = 1/2`
`sin pi/6 * sin theta + cos pi/6 * cos theta = 1/2`
`cos theta * cos pi/6 + sin theta * sin pi/6 = 1/2`
`cos (theta - pi/6) = cos (pi/3)`
The general solution is
`theta - pi/6 = 2"n"pi +- pi/3`, n ∈ Z
θ = `2"n"pi +- pi/3 + pi/6`, n ∈ Z
θ = `2"n"pi + pi/6 +- pi/3`, n ∈ Z
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