Question Number 106286 by bemath last updated on 04/Aug/20 $$\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right)+\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}\right)=\mathrm{arc}\:\mathrm{tan}\:\left(−\mathrm{7}\right) \\ $$$$\mathrm{for}\:\mathrm{x}\:\mathrm{real}\:\mathrm{number} \\ $$ Answered by bobhans last updated on 04/Aug/20 $$\rightarrow\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right)+\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}\right)=\mathrm{arc}\:\mathrm{tan}\:\left(−\mathrm{7}\right) \\ $$$$\mathrm{tan}\:\left(\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right)+\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}\right)\right)=\mathrm{tan}\:\left(\mathrm{arc}\:\mathrm{tan}\:\left(−\mathrm{7}\right)\right) \\…
Question Number 106220 by bemath last updated on 03/Aug/20 $$\mathrm{find}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{45}°\right)=\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{60}°\right) \\ $$ Answered by Dwaipayan Shikari last updated on 03/Aug/20 $${sin}\left(\frac{\pi}{\mathrm{2}}−{x}+\frac{\pi}{\mathrm{4}}\right)={sin}\left(\mathrm{2}{x}+\frac{\pi}{\mathrm{3}}\right) \\ $$$$\frac{\mathrm{3}\pi}{\mathrm{4}}−{x}=\mathrm{2}{k}\pi\pm\mathrm{2}{x}+\frac{\pi}{\mathrm{3}}\:\:\:\:\left({k}\in\mathbb{Z}\right) \\ $$$${first}\:{case}…
Question Number 106214 by john santu last updated on 03/Aug/20 $$\mathrm{solve}\::\:\mathrm{arc}\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{1}\right)=\:\mathrm{2arc}\:\mathrm{cos}\:\left(\mathrm{x}\right) \\ $$$$\mathrm{where}\:\mathrm{x}\:\mathrm{is}\:\mathrm{real}. \\ $$ Answered by bobhans last updated on 03/Aug/20 $$\Rightarrow\mathrm{cos}\:\left(\mathrm{arc}\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{1}\right)\right)=\:\mathrm{cos}\:\left(\mathrm{2}\:\mathrm{arc}\:\mathrm{cos}\:\left(\mathrm{x}\right)\right) \\ $$$$\Rightarrow\:\mathrm{x}−\mathrm{1}\:=\:\mathrm{2}\:\mathrm{cos}\:^{\mathrm{2}}…
Question Number 106196 by john santu last updated on 03/Aug/20 Commented by john santu last updated on 03/Aug/20 Commented by john santu last updated on…
Question Number 171719 by cortano1 last updated on 20/Jun/22 $$\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} {x}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:=\:\frac{\mathrm{48}}{\mathrm{35}} \\ $$ Commented by infinityaction last updated on 20/Jun/22 $$\mathrm{sin}\:{x}\:=\:\pm\frac{\mathrm{1}}{\mathrm{2}},\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$ Commented…
Question Number 40640 by upadhyayrakhi20@gmail.com last updated on 25/Jul/18 $${evaluate} \\ $$$$\mathrm{sin}\:\mathrm{72}\:^{.} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Jul/18 $${sin}\mathrm{72}={cos}\mathrm{18}=\sqrt{\mathrm{1}−{sin}^{\mathrm{2}} \mathrm{18}}\: \\ $$$${a}=\mathrm{18}^{\mathrm{0}}…
Question Number 171693 by cortano1 last updated on 20/Jun/22 Answered by som(math1967) last updated on 20/Jun/22 $$\:\:{tan}\mathrm{4}{x}=\frac{\mathrm{1}+{sinx}+{cosx}}{\mathrm{1}−{sinx}+{cosx}} \\ $$$$\Rightarrow\frac{{sin}\mathrm{4}{x}}{{cos}\mathrm{4}{x}}=\frac{\mathrm{1}+{sinx}+{cosx}}{\mathrm{1}−{sinx}+{cosx}} \\ $$$$\Rightarrow{sin}\mathrm{4}{x}−{sinxsin}\mathrm{4}{x}+{sin}\mathrm{4}{xcosx} \\ $$$$\:\:\:\:\:={cos}\mathrm{4}{x}+{sinxcos}\mathrm{4}{x}+{cos}\mathrm{4}{xcosx} \\ $$$$\Rightarrow{sin}\mathrm{4}{x}+{sin}\mathrm{4}{xcosx}−{sinxcos}\mathrm{4}{x}…
Question Number 106077 by bobhans last updated on 02/Aug/20 $$\mathcal{G}\mathrm{iven}\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{cos}\:^{\mathrm{2n}} \left(\theta\right)\:=\:\mathrm{5}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\mathrm{2}\theta+\mathrm{cos}\:\mathrm{4}\theta+\mathrm{cos}\:\mathrm{8}\theta+\mathrm{cos}\:\mathrm{16}\theta+\mathrm{cos} \\ $$$$\mathrm{32}\theta+…= \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{1}}{\mathrm{5}}\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{3}}{\mathrm{5}}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2}\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{1}\:\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{3} \\ $$ Terms of Service Privacy…
Question Number 171596 by nadovic last updated on 18/Jun/22 $${Show}\:{that}\:\frac{\mathrm{cos}\:\mathrm{70}°−\mathrm{cos}\:\mathrm{20}°}{\mathrm{sin}\:\mathrm{70}°−\mathrm{sin}\:\mathrm{20}°}\:=\:−\mathrm{1} \\ $$ Commented by mr W last updated on 18/Jun/22 $$\mathrm{cos}\:\mathrm{70}°=\mathrm{cos}\:\left(\mathrm{90}°−\mathrm{20}°\right)=\mathrm{sin}\:\mathrm{20}° \\ $$$$\mathrm{cos}\:\mathrm{20}°=\mathrm{cos}\:\left(\mathrm{90}°−\mathrm{70}°\right)=\mathrm{sin}\:\mathrm{70}° \\ $$$$\frac{\mathrm{cos}\:\mathrm{70}°−\mathrm{cos}\:\mathrm{20}°}{\mathrm{sin}\:\mathrm{70}°−\mathrm{sin}\:\mathrm{20}°}\:…
Question Number 171593 by cortano1 last updated on 18/Jun/22 $$\:{The}\:{maximum}\:{value}\:{of}\:{the} \\ $$$${expression}\:\mid\sqrt{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{2}{a}^{\mathrm{2}} }\:−\sqrt{\mathrm{2}{a}^{\mathrm{2}} −\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}}\:\mid\: \\ $$$${where}\:{a}\:{and}\:{x}\:{real}\:{numbers}\:{is}−−− \\ $$ Commented by infinityaction last updated…