Question Number 112075 by Aina Samuel Temidayo last updated on 06/Sep/20 $$\mathrm{Are}\:\mathrm{there}\:\mathrm{infinitely}\:\mathrm{many}\:\mathrm{solutions}\:\mathrm{to} \\ $$$$\mathrm{sin}\left(\frac{\beta}{\mathrm{2}}\right)=\mathrm{cos}\left(\mathrm{90}−\frac{\beta}{\mathrm{2}}\right)\:? \\ $$ Commented by $@y@m last updated on 06/Sep/20 This is an identity. �� https://en.m.wikipedia.org/wiki/Identity_(mathematics) Commented…
Question Number 112067 by bemath last updated on 06/Sep/20 $$\:\:\sqrt{{bemath}\:−−−−\blacksquare\blacksquare} \\ $$$${find}\:{the}\:{value}\:{of}\:\underset{{m}=\mathrm{1}} {\overset{\mathrm{6}} {\prod}}\mathrm{tan}\:\left(\frac{{m}\pi}{\mathrm{7}}\right).\: \\ $$ Commented by MJS_new last updated on 06/Sep/20 $$\mathrm{should}\:\mathrm{be}\:=\mathrm{0} \\…
Question Number 46478 by rahul 19 last updated on 27/Oct/18 $${If}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{1}.\:{Find}\:{range}\:{of}\: \\ $$$${E}\:=\:{x}^{\mathrm{3}} {y}+{xy}^{\mathrm{3}} +\mathrm{4}\:. \\ $$ Commented by rahul 19 last updated…
Question Number 46472 by peter frank last updated on 27/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 27/Oct/18 $$\left({asin}\theta+{bcos}\theta\right)^{\mathrm{2}} ={c}^{\mathrm{2}} \\ $$$${a}^{\mathrm{2}} {sin}^{\mathrm{2}} \theta+{b}^{\mathrm{2}} {cos}^{\mathrm{2}} \theta+\mathrm{2}{absin}\theta{cos}\theta={c}^{\mathrm{2}}…
Question Number 177542 by peter frank last updated on 06/Oct/22 Answered by Frix last updated on 07/Oct/22 $$\mathrm{9}°={x} \\ $$$$\mathrm{27}°=\mathrm{3}{x} \\ $$$$\mathrm{tan}\:\left(\mathrm{90}°−{x}\right)\:=\frac{\mathrm{1}}{\mathrm{tan}\:{x}} \\ $$$$\mathrm{81}°=\mathrm{90}°−\mathrm{9}° \\…
Question Number 177507 by peter frank last updated on 06/Oct/22 $$\mathrm{The}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{elevetion}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\: \\ $$$$\mathrm{A}\:\mathrm{in}\:\mathrm{the}\:\mathrm{north}\:\mathrm{is}\:\alpha\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tower} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\mathrm{B}\:\mathrm{in}\:\mathrm{the}\:\mathrm{east}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point} \\ $$$$\mathrm{A}\:\mathrm{is}\:\beta\:.\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{height} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tower}\:\mathrm{is}\: \\ $$$$\frac{\mathrm{ABsin}\:\alpha\mathrm{sin}\:\mathrm{B}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{2}}…
Question Number 46402 by scientist last updated on 25/Oct/18 $${show}\:{that}\:\mathrm{cos}\:\mathrm{7}\frac{\mathrm{1}}{\mathrm{2}}\:=\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}+\sqrt{\mathrm{6}} \\ $$ Commented by Meritguide1234 last updated on 25/Oct/18 $${it}\:{should}\:{be}\:{cot}\mathrm{7}\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by ajfour…
Question Number 46277 by rahul 19 last updated on 23/Oct/18 Commented by rahul 19 last updated on 23/Oct/18 $${this}\:{is}\:{possible}\:{only}\:{when}\:{sin}\mathrm{3}{x}=\mathrm{1} \\ $$$${and}\:{sin}\mathrm{7}{x}=\mathrm{1}…… \\ $$$$….. \\ $$…
Question Number 46283 by somil last updated on 23/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 23/Oct/18 $${PQ}=\mathrm{12}\:\:{QR}=\mathrm{5}\:\:{PR}=\sqrt{\mathrm{12}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} }\:=\mathrm{13} \\ $$$$ \\ $$$$ \\ $$$$\angle{DQP}=\theta\:\:\angle{DQR}=\mathrm{90}−\theta…
Question Number 111725 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{5}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{n}}\right)=\frac{\pi}{\mathrm{4}} \\ $$ Answered by $@y@m last updated…