Question Number 23648 by Tinkutara last updated on 03/Nov/17
$$\mathrm{If}\:\mathrm{sin}\left(\mathrm{3}\theta\:+\:\alpha\right)\:+\:\mathrm{sin}\left(\mathrm{3}\theta\:−\:\alpha\right)\:+\:\mathrm{sin}\left(\alpha\:−\:\theta\right) \\ $$$$−\:\mathrm{sin}\left(\alpha\:+\:\theta\right)\:=\:\mathrm{cos}\alpha\:\mathrm{and}\:\mathrm{cos}\alpha\:\neq\:\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{does}\:\mathrm{not}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{equation}? \\ $$$$\left(\mathrm{1}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{6}},\:{n}\:\in\:{I} \\ $$$$\left(\mathrm{2}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{10}},\:{n}\:\in\:{I} \\ $$$$\left(\mathrm{3}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{5}},\:{n}\:\in\:{I} \\ $$$$\left(\mathrm{4}\right)\:{n}\pi\:−\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\mathrm{3}\pi}{\mathrm{10}},\:{n}\:\in\:{I} \\ $$
Answered by Tinkutara last updated on 04/Nov/17
