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Category: Trigonometry

3cos-2-x-3cos-x-sin-x-2sin-x-1-x-0-2pi-

Question Number 95495 by i jagooll last updated on 25/May/20 $$\mathrm{3cos}\:^{\mathrm{2}} {x}\:−\:\mathrm{3cos}\:{x}\:\mathrm{sin}\:{x}\:+\:\mathrm{2sin}\:{x}\:=\:\mathrm{1} \\ $$$${x}\:\in\:\left[\:\mathrm{0},\:\mathrm{2}\pi\:\right]\: \\ $$ Answered by bobhans last updated on 25/May/20 $$\mathrm{3}−\mathrm{3sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3sin}\:\mathrm{xcos}\:\mathrm{x}\:+\mathrm{2sin}\:\mathrm{x}\:=\:\mathrm{1}…

0-pi-find-he-values-of-n-1-1-n-cos-n-and-n-1-1-n-sin-n-

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:…

find-1-cos-4-pi-9-1-cos-4-3pi-9-1-cos-4-5pi-9-1-cos-4-7pi-9-

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}…

find-cos-4-pi-8-cos-4-3pi-8-cos-4-5pi-8-cos-4-7pi-8-

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}}…