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Question Number 23648 by Tinkutara last updated on 03/Nov/17

If sin(3θ + α) + sin(3θ − α) + sin(α − θ) − sin(α + θ) = cosα and cosα ≠ 0, then which of the values of θ does not satisfy the given equation? (1) nπ + (−1)^n (π/6), n ∈ I (2) nπ + (−1)^n (π/(10)), n ∈ I (3) nπ + (−1)^n (π/5), n ∈ I (4) nπ − (−1)^n ((3π)/(10)), n ∈ I

$$\mathrm{If}\:\mathrm{sin}\left(\mathrm{3}\theta\:+\:\alpha\right)\:+\:\mathrm{sin}\left(\mathrm{3}\theta\:−\:\alpha\right)\:+\:\mathrm{sin}\left(\alpha\:−\:\theta\right) \\ $$$$−\:\mathrm{sin}\left(\alpha\:+\:\theta\right)\:=\:\mathrm{cos}\alpha\:\mathrm{and}\:\mathrm{cos}\alpha\:\neq\:\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{does}\:\mathrm{not}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{equation}? \\ $$$$\left(\mathrm{1}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{6}},\:{n}\:\in\:{I} \\ $$$$\left(\mathrm{2}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{10}},\:{n}\:\in\:{I} \\ $$$$\left(\mathrm{3}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{5}},\:{n}\:\in\:{I} \\ $$$$\left(\mathrm{4}\right)\:{n}\pi\:−\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\mathrm{3}\pi}{\mathrm{10}},\:{n}\:\in\:{I} \\ $$

Answered by Tinkutara last updated on 04/Nov/17

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