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Category: Trigonometry

prove-sin18-cos36-1-4-

Question Number 57474 by malwaan last updated on 05/Apr/19 $$\mathrm{prove}\: \\ $$$$\boldsymbol{{sin}}\mathrm{18}×\boldsymbol{{cos}}\mathrm{36}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Commented by Abdo msup. last updated on 05/Apr/19 $$\mathrm{18}\rightarrow{x} \\ $$$$\mathrm{180}\rightarrow\pi\:\Rightarrow\mathrm{180}{x}\:=\mathrm{18}\pi\:\Rightarrow{x}\:=\frac{\pi}{\mathrm{10}}\:\Rightarrow\mathrm{36}\:=\frac{\pi}{\mathrm{5}}…

sin-pi-2-4x-x-cos-pi-x-7-x-1-x-

Question Number 188475 by cortano12 last updated on 02/Mar/23 $$\:\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}\left(\mathrm{4x}+\sqrt{\mathrm{x}}\:\right)\right)\mathrm{cos}\:\left(\pi\left(\mathrm{x}+\mathrm{7}\sqrt{\mathrm{x}}\right)\right)=\mathrm{1} \\ $$$$\:\mathrm{x}=? \\ $$ Answered by Frix last updated on 02/Mar/23 $$\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:=\mathrm{1} \\ $$$$\Leftrightarrow \\…

Question-188376

Question Number 188376 by Rupesh123 last updated on 28/Feb/23 Answered by Frix last updated on 28/Feb/23 $$\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{7}}\:\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\:\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\:= \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{7}}\:+\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\:−\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\right) \\ $$$$\left(\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{7}}\:\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\:\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\right)^{\mathrm{3}} = \\ $$$$=\frac{\mathrm{7}}{\mathrm{256}}\left(\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{7}}\:+\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\:−\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\right) \\…

1-18log10000-43x-12-2-43x-18log1000-3-18log10000-43x-4-18log10000-43x-5-log-sinx-sin-log100-6-log-sinx-12-7-x-2-x-90-8-log-sin-pi-4-

Question Number 188281 by mathlove last updated on 27/Feb/23 $$\left.\mathrm{1}\right)\:\:\frac{\mathrm{18}{log}\mathrm{10000}+\sqrt{\mathrm{43}{x}}}{\mathrm{12}} \\ $$$$\left.\mathrm{2}\right)\:\frac{\sqrt{\mathrm{43}{x}}}{\mathrm{18}{log}\mathrm{1000}} \\ $$$$\left.\mathrm{3}\right)\:\:\mathrm{18}{log}\mathrm{10000}+\sqrt{\mathrm{43}{x}}\:\:\: \\ $$$$\left.\mathrm{4}\right)\:\:\:\frac{\mathrm{18}{log}\mathrm{10000}}{\:\sqrt{\mathrm{43}{x}}} \\ $$$$\left.\mathrm{5}\right)\:\:\:{log}\left({sinx}\right)+{sin}\left({log}\mathrm{100}\right) \\ $$$$\left.\mathrm{6}\right)\:\:\:{log}\left({sinx}\right)+\mathrm{12} \\ $$$$\left.\mathrm{7}\right)\:\:\:\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{90}} \\ $$$$\left.\mathrm{8}\right)\:\:{log}\left({sin}\frac{\pi}{\mathrm{4}}\right)+\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}…

Question-188209

Question Number 188209 by Rupesh123 last updated on 26/Feb/23 Answered by Ezzat last updated on 26/Feb/23 $$\left(\mathrm{2}\:{R}\:{sinB}\:\right)^{\mathrm{2}} .{sin}^{\mathrm{2}} \left({A}\right)−\left(\:\mathrm{2}\:{R}\:{sinA}\right)^{\mathrm{2}} \:{sin}^{\mathrm{2}} {B}\:=\mathrm{48}\:−{a}^{\mathrm{2}} \\ $$$$\mathrm{4}\:{R}^{\mathrm{2}} \:{sin}^{\mathrm{2}} {B}\:.{sin}^{\mathrm{2}}…