Question Number 29848 by abdo imad last updated on 12/Feb/18 $${find}\:\:\sum_{{k}=\mathrm{0}} ^{{n}} {cos}\left({kx}\right)\:{and}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{sin}\left({kx}\right)\:. \\ $$ Commented by Tinkutara last updated on 13/Feb/18 $$\mathrm{1}+\mathrm{cos}\:{x}+\mathrm{cos}\:\mathrm{2}{x}+…+\mathrm{cos}\:{nx}…
Question Number 29847 by abdo imad last updated on 12/Feb/18 $$\left.\theta\:\in\right]\mathrm{0},\pi\left[\:\:\:{find}\:{he}\:{values}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{cos}\left({n}\theta\right)\:{and}\right. \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{sin}\left({n}\theta\right)\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 29834 by abdo imad last updated on 12/Feb/18 $${find}\:\:\:\:\frac{\mathrm{1}}{{cos}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{9}}\right)}\:+\frac{\mathrm{1}}{{cos}^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{9}}\right)}\:+\:\frac{\mathrm{1}}{{cos}^{\mathrm{4}} \left(\frac{\mathrm{5}\pi}{\mathrm{9}}\right)}\:+\frac{\mathrm{1}}{{cos}^{\mathrm{4}} \left(\frac{\mathrm{7}\pi}{\mathrm{9}}\right)}\:. \\ $$ Commented by MJS last updated on 14/Feb/18 $$=\mathrm{1120}\:\mathrm{but}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{quite}\:\mathrm{some}…
Question Number 29833 by abdo imad last updated on 12/Feb/18 $${find}\:\:{cos}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{5}\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right). \\ $$ Answered by MJS last updated on 14/Feb/18 $$\mathrm{cos}\left(\frac{\pi}{\mathrm{8}}\right)=−\mathrm{cos}\left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right)=\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}{\mathrm{2}}…
Question Number 29821 by Victor31926 last updated on 12/Feb/18 $$\frac{\mathrm{sin}\:\mathrm{16x}}{\mathrm{sin}\:\mathrm{x}}\:\:\:\:\:\:?\mathrm{pls}\:\mathrm{help}. \\ $$ Commented by abdo imad last updated on 13/Feb/18 $${what}\:{is}\:{the}\:{question}\:? \\ $$ Commented by…
Question Number 95326 by bobhans last updated on 24/May/20 $$\mathrm{sin}\:\mathrm{72}^{\mathrm{o}} \:=\:\mathrm{p}\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{48}^{\mathrm{o}} \\ $$$$\mathrm{find}\:\mathrm{tan}\:\mathrm{12}^{\mathrm{o}} \:? \\ $$ Commented by mr W last updated on 24/May/20 $$\mathrm{sin}\:\mathrm{72}°=\mathrm{sin}\:\left(\mathrm{60}°+\mathrm{12}°\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\sqrt{\mathrm{3}}\mathrm{cos}\:\mathrm{12}°+\mathrm{sin}\:\mathrm{12}°\right)…
Question Number 160815 by cortano last updated on 07/Dec/21 $$\:\:\:\:\mathrm{sec}\:\left(\mathrm{3x}\right)−\mathrm{6cos}\:\left(\mathrm{3x}\right)=\mathrm{4sin}\:\left(\mathrm{3x}\right) \\ $$$$\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$ Commented by blackmamba last updated on 07/Dec/21 $$\:\Rightarrow\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{3}{x}}\:−\mathrm{6cos}\:\mathrm{3}{x}\:=\:\mathrm{4sin}\:\mathrm{3}{x}\: \\ $$$$\Rightarrow\frac{\mathrm{1}}{{t}}\:−\:\mathrm{6}{t}\:=\:\mathrm{4}\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }\:;\:\left[\:{t}\:=\:\mathrm{cos}\:\mathrm{3}{x}\:\right]…
Question Number 160762 by mathlove last updated on 06/Dec/21 $$\mathrm{sin}\:\mathrm{10}+\mathrm{sin}\:\mathrm{20}+\mathrm{sin}\:\mathrm{30}+\mathrm{sin}\:\mathrm{40}+\centerdot\centerdot\centerdot\centerdot+\mathrm{sin}\:\mathrm{360}=? \\ $$ Commented by som(math1967) last updated on 06/Dec/21 $$\mathrm{0} \\ $$ Commented by mathlove…
Question Number 29658 by gyugfeet last updated on 11/Feb/18 $${tan}\theta+{tan}\mathrm{2}\theta+\sqrt{\mathrm{3}}\:{tan}\theta.{tan}\mathrm{2}\theta=\sqrt{\mathrm{3}}\:\:\:\:\:\left(\mathrm{0}^{{o}\:} \leqslant\theta\leqslant\mathrm{360}\right) \\ $$ Answered by mrW2 last updated on 11/Feb/18 $${tan}\theta+{tan}\mathrm{2}\theta=\sqrt{\mathrm{3}}\left(\mathrm{1}−\:{tan}\theta.{tan}\mathrm{2}\theta\right) \\ $$$$\frac{\mathrm{tan}\:\theta+\mathrm{tan}\:\mathrm{2}\theta}{\mathrm{1}−\mathrm{tan}\:\theta\:\mathrm{tan}\:\mathrm{2}\theta}=\sqrt{\mathrm{3}} \\ $$$$\mathrm{tan}\:\mathrm{3}\theta=\sqrt{\mathrm{3}}…
Question Number 29581 by math solver last updated on 10/Feb/18 $${Let}\:{x}\:=\:\mathrm{4}{sin}^{\mathrm{2}} \mathrm{10}^{{o}} +\mathrm{4}{sin}^{\mathrm{2}} \mathrm{50}^{{o}} {cos}\mathrm{20}^{{o}} +{cos}\mathrm{80}^{{o}} \\ $$$${and}\:{y}\:=\:{cos}^{\mathrm{2}} \:\frac{\pi}{\mathrm{5}}+{cos}^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{15}}+{cos}^{\mathrm{2}} \frac{\mathrm{8}\pi}{\mathrm{15}}. \\ $$$${find}\:{x}+{y}\:? \\ $$…