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Question
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
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Solution
We know that, `cos pi/(3) = 1/2` and cos(2π - θ) = cosθ
`∴ cos π/3 = cos(2pi - pi/3) = cos (5pi)/3`
`∴ cos pi/3 = cos (5pi)/3 = 1/2`, where
`0 < pi/3 < 2pi and 0 < (5pi)/3 < 2pi`
`∴ cosθ = 1/2 "gives" cosθ = cos pi/(3) = cos (5pi)/(3)`
∴ θ = `pi/(3) and θ = (5pi)/(3)`
Hence, the required principal solutions are
`θ = pi/(3) and θ = (5pi)/(3)`.
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