Question Number 133587 by bemath last updated on 23/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\mathrm{12}°\:. \\ $$ Answered by Dwaipayan Shikari last updated on 23/Feb/21 $${sin}\frac{\pi}{\mathrm{60}}={sin}\frac{\pi}{\mathrm{10}}{cos}\frac{\pi}{\mathrm{12}}−{sin}\frac{\pi}{\mathrm{12}}{cos}\frac{\pi}{\mathrm{10}} \\ $$$$=\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}.\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}{\mathrm{2}}−\frac{\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}}.\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}{\mathrm{2}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{16}}\left(\left(\sqrt{\mathrm{5}}−\mathrm{1}\right)\left(\sqrt{\mathrm{6}}−\sqrt{\mathrm{2}}\right)−\left(\sqrt{\mathrm{6}}+\sqrt{\mathrm{2}}\right)\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}\right)…
Question Number 68022 by anaplak last updated on 03/Sep/19 Commented by anaplak last updated on 08/Sep/19 $${your}\:{given}\:{solution}\:{is}\:{not}\:{right}\:{according}\:{to}\:{my}\:{question}\:.. \\ $$ Answered by mr W last updated…
Question Number 68021 by anaplak last updated on 03/Sep/19 Commented by Tanmay chaudhury last updated on 03/Sep/19 Answered by Tanmay chaudhury last updated on 03/Sep/19…
Question Number 133444 by mnjuly1970 last updated on 22/Feb/21 Answered by guyyy last updated on 22/Feb/21 Commented by mnjuly1970 last updated on 23/Feb/21 $${thank}\:{you}\:{so}\:{much}… \\…
Question Number 133443 by mnjuly1970 last updated on 22/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……{nice}\:\:\:\:\:\:{calculus}……. \\ $$$$\:\:{if}\:\:{a},{b},{c}\:\geqslant\mathrm{0} \\ $$$$\:\:\:\:{and}\:::\:\:\:\:{acos}^{\mathrm{2}} \left({x}\right)+{bsin}^{\mathrm{2}} \left({x}\right)\leqslant{c} \\ $$$$\:\:\:\:{then}\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\:\:\sqrt{{a}}\:{cos}^{\mathrm{2}} \left({x}\right)+\sqrt{{b}}\:{sin}^{\mathrm{2}} \left({x}\right)\leqslant\sqrt{{c}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…………. \\…
Question Number 133351 by bramlexs22 last updated on 21/Feb/21 Answered by mr W last updated on 22/Feb/21 $${a}=\mathrm{1},\:{b}=\mathrm{2},\:{c}=\sqrt{\mathrm{5}} \\ $$$$\Rightarrow{A}=\mathrm{1} \\ $$ Terms of Service…
Question Number 133347 by rs4089 last updated on 21/Feb/21 $${for}\:{a}\:{triangle}\:{ABC}\:… \\ $$$${find}\:{minimum}\:{value}\:{of}\: \\ $$$${CosA}.{CosB}.{CosC} \\ $$ Commented by mr W last updated on 21/Feb/21 $${i}\:{think}\:{there}\:{is}\:{no}\:{minimum},…
Question Number 133142 by bemath last updated on 19/Feb/21 $$\mathrm{If}\:\mathrm{sin}\:\left(\frac{\mathrm{23}\pi}{\mathrm{24}}\right)\:=\:\sqrt{\frac{\mathrm{2}\sqrt{\mathrm{p}}−\sqrt{\mathrm{q}}−\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{r}}}} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} \right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\: \\ $$ Answered by Ñï= last updated on…
Question Number 67495 by TawaTawa last updated on 28/Aug/19 Commented by Prithwish sen last updated on 28/Aug/19 $$\mathrm{sin}\left(\frac{\mathrm{5}}{\mathrm{2}}\pi+\mathrm{x}\right)=\mathrm{Cos}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{9}}\right)\Rightarrow\mathrm{Cosx}=\mathrm{Cos}\left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{18}}\right) \\ $$$$\mathrm{x}=\mathrm{2n}\pi\pm\left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{18}}\right)\:\:\:\mathrm{n}\in\:\mathbb{Z} \\ $$ Commented by TawaTawa…
Question Number 1961 by alib last updated on 26/Oct/15 $${Solve}… \\ $$$$ \\ $$$$\mathrm{1}+\:{sin}\:\mathrm{2}{x}\:=\:{sin}\:{x}\:+\:{cos}\:{x} \\ $$ Answered by Rasheed Soomro last updated on 26/Oct/15 $$\mathrm{1}+\:{sin}\:\mathrm{2}{x}\:=\:{sin}\:{x}\:+\:{cos}\:{x}…