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Category: Trigonometry

Question-154748

Question Number 154748 by imjagoll last updated on 21/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 21/Sep/21 $$\mathrm{sin}\left(\mathrm{3log}_{\left(\mathrm{2sin}{x}\right)} \sqrt[{\mathrm{3}}]{\pi}\right)=\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\mathrm{log}_{\left(\mathrm{2sin}{x}\right)} \pi=\frac{\pi}{\mathrm{6}} \\ $$$$\Rightarrow\mathrm{log}_{\pi} \left(\mathrm{2sin}{x}\right)=\frac{\mathrm{6}}{\pi}\:\Rightarrow\mathrm{sin}{x}=\frac{\mathrm{1}}{\mathrm{2}}\pi^{\frac{\mathrm{6}}{\pi}} \\ $$$$\Rightarrow{x}=\mathrm{arcsin}\left(\frac{\mathrm{1}}{\mathrm{2}}\pi^{\frac{\mathrm{6}}{\pi}} \right)…

cos-x-sin-x-1-2-cos-x-sin-x-3-8-pi-lt-x-lt-2pi-cos-x-sin-x-

Question Number 89193 by jagoll last updated on 16/Apr/20 $$\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}\:=\:\frac{\mathrm{3}}{\mathrm{8}}\:,\:\pi\:<\:{x}\:<\:\mathrm{2}\pi \\ $$$$\mathrm{cos}\:{x}\:+\:\mathrm{sin}\:{x}\:=? \\ $$ Commented by Tony Lin last updated on 16/Apr/20 $$\because\pi<{x}<\mathrm{2}\pi…

If-sin-3-sin-3-sin-sin-cos-and-cos-0-then-which-of-the-values-of-does-not-satisfy-the-given-equation-1-npi-1-n-pi-6-n-I-2-npi-1-n-pi-10-

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}…

cos-4x-1-cos-2x-1-cos-x-1-1-8-0-x-2pi-

Question Number 89079 by john santu last updated on 15/Apr/20 $$\left(\mathrm{cos}\:\mathrm{4}{x}+\mathrm{1}\right)\left(\mathrm{cos}\:\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{cos}\:{x}+\mathrm{1}\right)=\:\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$\mathrm{0}\:\leqslant\:{x}\:\leqslant\:\mathrm{2}\pi \\ $$ Answered by TANMAY PANACEA. last updated on 15/Apr/20 $$\mathrm{2}{cos}^{\mathrm{2}} \mathrm{2}{x}.\mathrm{2}{cos}^{\mathrm{2}}…

cos-x-sin-x-4-5-5sin-x-

Question Number 89047 by jagoll last updated on 15/Apr/20 $$\mathrm{cos}\:{x}+\mathrm{sin}\:{x}=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\mathrm{5sin}\:{x}\:=\:? \\ $$ Commented by john santu last updated on 15/Apr/20 $$\pm\:\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}}\:=\:\frac{\mathrm{4}}{\mathrm{5}}−\mathrm{sin}\:{x} \\…