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Question
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
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Solution
We have sin θ + sin 3θ + sin 5θ = 0
∴ (sin θ + sin 5θ) + sin 3θ = 0
∴ 2 sin 3θ × cos 2θ + sin 3θ = 0
∴ (2 cos 2θ + 1) sin 3θ = 0
∴ sin 3θ = 0 or cos 2θ = `-1/2`
∴ sin 3θ = 0 or cos 2θ = `cos (2π)/3`
∴ 3θ = nπ or 2θ = `2nπ ± (2π)/3`, where n ∈ Z.
θ = `(nπ)/3` or θ = `nπ ± π/3`,
where n ∈ Z is the required general solution.
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