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Question Number 208912 by dimentri last updated on 27/Jun/24 $$\:\:\:\underbrace{\Subset} \underbrace{ \cancel{} }\pi \\ $$ Commented by Frix last updated on 27/Jun/24 $$\mathrm{33} \\ $$…
Question Number 208755 by efronzo1 last updated on 22/Jun/24 Answered by mr W last updated on 22/Jun/24 Commented by mr W last updated on 22/Jun/24…
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Question Number 208437 by efronzo1 last updated on 16/Jun/24 Answered by som(math1967) last updated on 16/Jun/24 $$\:{a}={sin}\mathrm{84}+{cos}\mathrm{66} \\ $$$$\Rightarrow{a}={sin}\mathrm{84}+{sin}\mathrm{24} \\ $$$$\Rightarrow{a}=\mathrm{2}{sin}\mathrm{54}{cos}\mathrm{30} \\ $$$$\:\therefore{a}=\mathrm{2}×\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{4}}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}=\frac{\sqrt{\mathrm{3}}\left(\sqrt{\mathrm{5}}+\mathrm{1}\right)}{\mathrm{4}} \\ $$$${b}={sin}\mathrm{48}−{sin}\mathrm{12}…
Question Number 208252 by efronzo1 last updated on 09/Jun/24 $$\:\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{8}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{10}\pi}{\mathrm{22}}\right)\mathrm{cos}\:\left(\frac{\mathrm{16}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{20}\pi}{\mathrm{21}}\right)=? \\ $$ Answered by som(math1967) last updated on 09/Jun/24 $$\:{let}\:\frac{\pi}{\mathrm{21}}={x} \\ $$$${cos}\mathrm{2}{xcos}\mathrm{4}{xcos}\mathrm{8}{xcos}\mathrm{10}{xcos}\mathrm{16}{xcos}\mathrm{20}{x} \\ $$$${cosxcos}\mathrm{2}{xcos}\mathrm{4}{xcos}\mathrm{8}{xcos}\mathrm{10}{xcos}\mathrm{5}{x} \\…
Question Number 208130 by efronzo1 last updated on 06/Jun/24 $$\:\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{3x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{5x}}\:+ \\ $$$$\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{7x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{11x}}=?\: \\ $$ Answered by Ghisom last updated on 06/Jun/24 $$\mathrm{let}\:{c}_{{n}} =\mathrm{cos}\:{nx} \\ $$$$=−\frac{\mathrm{2}{c}_{\mathrm{10}}…
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