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cosxcos-pi-6-sin-pi-6-sinx-pi-4-

Question Number 167986 by DAVONG last updated on 31/Mar/22 $$\mathrm{cosxcos}\frac{\pi}{\mathrm{6}}−\mathrm{sin}\frac{\pi}{\mathrm{6}}\mathrm{sinx}=\frac{\pi}{\mathrm{4}} \\ $$ Answered by Rasheed.Sindhi last updated on 31/Mar/22 $$\mathrm{cosxcos}\frac{\pi}{\mathrm{6}}−\mathrm{sin}\frac{\pi}{\mathrm{6}}\mathrm{sinx}=\frac{\pi}{\mathrm{4}} \\ $$$$\Rightarrow\mathrm{cos}\left({x}+\frac{\pi}{\mathrm{6}}\right)=\frac{\pi}{\mathrm{4}}\: \\ $$$$\:\:\:\:\:{x}+\frac{\pi}{\mathrm{6}}=\mathrm{cos}^{−\mathrm{1}} \left(\frac{\pi}{\mathrm{4}}\right)…

prove-a-2-b-2-sin-cos-ab-a-2-b-2-cos-2-b-2-asin-bcos-acos-bsin-

Question Number 167929 by Huy last updated on 29/Mar/22 $${prove}:\: \\ $$$$\:\:\:\:\:\:\:\frac{\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\mathrm{sin}\alpha\mathrm{cos}\alpha−{ab}}{\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \alpha−{b}^{\mathrm{2}} }=\frac{{a}\mathrm{sin}\alpha−{b}\mathrm{cos}\alpha}{{a}\mathrm{cos}\alpha+{b}\mathrm{sin}\alpha} \\ $$ Answered by som(math1967) last updated…

Given-f-x-ax-5-bx-4-cx-3-dx-2-ex-f-f-1-1-f-2-1-4-f-3-1-9-f-4-1-16-f-5-1-25-and-f-6-1-36-Value-of-f-8-

Question Number 167925 by naka3546 last updated on 29/Mar/22 $$\mathrm{Given}\:\:{f}\left({x}\right)\:=\:{ax}^{\mathrm{5}} \:+\:{bx}^{\mathrm{4}} \:+\:{cx}^{\mathrm{3}} \:+\:{dx}^{\mathrm{2}} \:+\:{ex}\:+\:{f}\:. \\ $$$${f}\left(\mathrm{1}\right)\:=\:\mathrm{1}\:,\:{f}\left(\mathrm{2}\right)\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\:,\:\:{f}\left(\mathrm{3}\right)\:=\:\frac{\mathrm{1}}{\mathrm{9}}\:\:,\:\:{f}\left(\mathrm{4}\right)\:=\:\frac{\mathrm{1}}{\mathrm{16}}\:\:, \\ $$$${f}\left(\mathrm{5}\right)\:=\:\frac{\mathrm{1}}{\mathrm{25}}\:\:,\:\:{and}\:\:{f}\left(\mathrm{6}\right)\:=\:\frac{\mathrm{1}}{\mathrm{36}}\:. \\ $$$${Value}\:\:{of}\:\:{f}\left(\mathrm{8}\right)\:=\:? \\ $$ Answered by mr…

give-z-cos-2pi-2015-isin-2pi-2015-find-S-1-z-z-2-z-3-z-2014-

Question Number 167916 by bounhome last updated on 29/Mar/22 $${give}:\:{z}={cos}\left(\frac{\mathrm{2}\pi}{\mathrm{2015}}\right)+{isin}\left(\frac{\mathrm{2}\pi}{\mathrm{2015}}\right) \\ $$$${find}\:{S}=\mathrm{1}+{z}+{z}^{\mathrm{2}} +{z}^{\mathrm{3}} +…+{z}^{\mathrm{2014}} \\ $$ Commented by benhamimed last updated on 29/Mar/22 $${z}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{2015}}} \\…