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Category: Trigonometry

I-would-like-that-you-help-me-to-show-this-equality-16cos-24-cos-5-24-cos-7-24-cos-11-24-1-

Question Number 75048 by mathocean1 last updated on 06/Dec/19 $$\mathrm{I}\:\mathrm{would}\:\mathrm{like}\:\mathrm{that}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\: \\ $$$$\mathrm{show}\:\mathrm{this}\:\mathrm{equality}: \\ $$$$\mathrm{16cos}\:\frac{\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{5}\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{7}\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{11}\Pi}{\mathrm{24}}=\mathrm{1} \\ $$ Commented by mind is power last updated on 06/Dec/19…

Please-can-you-help-me-to-to-show-that-cos-47-13-sin-23-26-sin-3-26-

Question Number 75040 by mathocean1 last updated on 06/Dec/19 $$\mathrm{Please}\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\: \\ $$$$\mathrm{to}\:\mathrm{show}\:\mathrm{that}: \\ $$$$\mathrm{cos}\:\frac{\mathrm{47}\Pi}{\mathrm{13}}=\mathrm{sin}\:\frac{\mathrm{23}\Pi}{\mathrm{26}}=\mathrm{sin}\frac{\mathrm{3}\Pi}{\mathrm{26}} \\ $$ Answered by Kunal12588 last updated on 06/Dec/19 $${cos}\frac{\mathrm{47}\pi}{\mathrm{13}}={cos}\left(\frac{\mathrm{52}\pi−\mathrm{5}\pi}{\mathrm{13}}\right)={cos}\left(\mathrm{4}\pi−\frac{\mathrm{5}\pi}{\mathrm{13}}\right) \\…

arctan-1-3-arctan-1-4-arctan-1-5-arctan-1-n-pi-4-So-1-n-

Question Number 9486 by Joel575 last updated on 10/Dec/16 $$\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{3}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{4}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{{n}}\:=\:\frac{\pi}{\mathrm{4}} \\ $$$$\mathrm{So},\:\frac{\mathrm{1}}{{n}}\:=\:? \\ $$ Answered by mrW last updated on 10/Dec/16 $$\mathrm{tan}\:\left(\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{3}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{4}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{{n}}\right)\:=\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}\:}\right) \\ $$$$\frac{\mathrm{tan}\:\left(\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{3}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{4}}\right)+\mathrm{tan}\:\left(\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{n}}\right)}{\mathrm{1}−\mathrm{tan}\:\left(\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{3}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{4}}\right)×\mathrm{tan}\:\left(\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\mathrm{arctan}\:\frac{\mathrm{1}}{{n}}\right)\:}=\mathrm{1} \\…

A-triangle-is-inscribed-in-a-circle-the-vertices-of-the-triangle-divided-the-circumference-of-the-circle-into-three-area-of-length-6-8-10-units-then-the-area-of-triangle-is-equal-to-a-64-3-

Question Number 140533 by liberty last updated on 09/May/21 $$\mathrm{A}\:\mathrm{triangle}\:\mathrm{is}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}. \\ $$$$\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{divided} \\ $$$$\mathrm{the}\:\mathrm{circumference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{into}\:\mathrm{three}\:\mathrm{area}\:\mathrm{of}\:\mathrm{length}\:\mathrm{6},\mathrm{8},\mathrm{10} \\ $$$$\mathrm{units}\:\mathrm{then}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{triangle} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to}… \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{64}\sqrt{\mathrm{3}}\left(\sqrt{\mathrm{3}}+\mathrm{1}\right)}{\pi^{\mathrm{2}} }\:\:\:\:\left(\mathrm{c}\right)\:\frac{\mathrm{36}\sqrt{\mathrm{3}}\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)}{\pi^{\mathrm{2}} } \\…

If-sin-2A-sin-2B-Prove-that-tan-A-B-tan-A-B-1-1-

Question Number 74966 by ajfour last updated on 05/Dec/19 $${If}\:\:\mathrm{sin}\:\mathrm{2}{A}=\lambda\mathrm{sin}\:\mathrm{2}{B} \\ $$$${Prove}\:{that}\:\:\frac{\mathrm{tan}\:\left({A}+{B}\right)}{\mathrm{tan}\:\left({A}−{B}\right)}=\frac{\lambda+\mathrm{1}}{\lambda−\mathrm{1}}\:. \\ $$ Commented by Prithwish sen last updated on 05/Dec/19 $$\frac{\mathrm{sin2A}}{\mathrm{sin2B}}\:=\:\lambda \\ $$$$\frac{\mathrm{sin2A}+\mathrm{sin2B}}{\mathrm{sin2A}−\mathrm{sin2B}}\:=\:\frac{\lambda+\mathrm{1}}{\lambda−\mathrm{1}}…

tan-1-1-x-1-x-cot-1-1-x-1-x-pi-2-x-

Question Number 140494 by benjo_mathlover last updated on 08/May/21 $$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)+\mathrm{cot}^{−\mathrm{1}} \left(\frac{\mathrm{1}+\mathrm{x}}{\mathrm{1}−\mathrm{x}}\right)=\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{x}=? \\ $$ Answered by john_santu last updated on 08/May/21 $$\Rightarrow\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)=\frac{\pi}{\mathrm{2}}−\mathrm{cot}^{−\mathrm{1}}…

tanA-cot-A-2cosec2A-

Question Number 9414 by Rohit kumar last updated on 06/Dec/16 $${tanA}+{cot}={A}=\:\mathrm{2}{cosec}\mathrm{2}{A} \\ $$ Answered by ridwan balatif last updated on 06/Dec/16 $$\mathrm{tanA}+\mathrm{cotA}=\mathrm{2cosec2A} \\ $$$$\frac{\mathrm{sinA}}{\mathrm{cosA}}+\frac{\mathrm{cosA}}{\mathrm{sinA}}=\mathrm{2cosec2A} \\…