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Category: Trigonometry

find-cos-4-pi-8-cos-4-3pi-8-cos-4-5pi-8-cos-4-7pi-8-

Question Number 29833 by abdo imad last updated on 12/Feb/18 $${find}\:\:{cos}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{5}\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right). \\ $$ Answered by MJS last updated on 14/Feb/18 $$\mathrm{cos}\left(\frac{\pi}{\mathrm{8}}\right)=−\mathrm{cos}\left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right)=\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}{\mathrm{2}}…

sin-72-o-p-3-cos-48-o-find-tan-12-o-

Question Number 95326 by bobhans last updated on 24/May/20 $$\mathrm{sin}\:\mathrm{72}^{\mathrm{o}} \:=\:\mathrm{p}\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{48}^{\mathrm{o}} \\ $$$$\mathrm{find}\:\mathrm{tan}\:\mathrm{12}^{\mathrm{o}} \:? \\ $$ Commented by mr W last updated on 24/May/20 $$\mathrm{sin}\:\mathrm{72}°=\mathrm{sin}\:\left(\mathrm{60}°+\mathrm{12}°\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\sqrt{\mathrm{3}}\mathrm{cos}\:\mathrm{12}°+\mathrm{sin}\:\mathrm{12}°\right)…

sec-3x-6cos-3x-4sin-3x-find-the-solution-

Question Number 160815 by cortano last updated on 07/Dec/21 $$\:\:\:\:\mathrm{sec}\:\left(\mathrm{3x}\right)−\mathrm{6cos}\:\left(\mathrm{3x}\right)=\mathrm{4sin}\:\left(\mathrm{3x}\right) \\ $$$$\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$ Commented by blackmamba last updated on 07/Dec/21 $$\:\Rightarrow\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{3}{x}}\:−\mathrm{6cos}\:\mathrm{3}{x}\:=\:\mathrm{4sin}\:\mathrm{3}{x}\: \\ $$$$\Rightarrow\frac{\mathrm{1}}{{t}}\:−\:\mathrm{6}{t}\:=\:\mathrm{4}\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }\:;\:\left[\:{t}\:=\:\mathrm{cos}\:\mathrm{3}{x}\:\right]…

tan-tan2-3-tan-tan2-3-0-o-360-

Question Number 29658 by gyugfeet last updated on 11/Feb/18 $${tan}\theta+{tan}\mathrm{2}\theta+\sqrt{\mathrm{3}}\:{tan}\theta.{tan}\mathrm{2}\theta=\sqrt{\mathrm{3}}\:\:\:\:\:\left(\mathrm{0}^{{o}\:} \leqslant\theta\leqslant\mathrm{360}\right) \\ $$ Answered by mrW2 last updated on 11/Feb/18 $${tan}\theta+{tan}\mathrm{2}\theta=\sqrt{\mathrm{3}}\left(\mathrm{1}−\:{tan}\theta.{tan}\mathrm{2}\theta\right) \\ $$$$\frac{\mathrm{tan}\:\theta+\mathrm{tan}\:\mathrm{2}\theta}{\mathrm{1}−\mathrm{tan}\:\theta\:\mathrm{tan}\:\mathrm{2}\theta}=\sqrt{\mathrm{3}} \\ $$$$\mathrm{tan}\:\mathrm{3}\theta=\sqrt{\mathrm{3}}…

Let-x-4sin-2-10-o-4sin-2-50-o-cos20-o-cos80-o-and-y-cos-2-pi-5-cos-2-2pi-15-cos-2-8pi-15-find-x-y-

Question Number 29581 by math solver last updated on 10/Feb/18 $${Let}\:{x}\:=\:\mathrm{4}{sin}^{\mathrm{2}} \mathrm{10}^{{o}} +\mathrm{4}{sin}^{\mathrm{2}} \mathrm{50}^{{o}} {cos}\mathrm{20}^{{o}} +{cos}\mathrm{80}^{{o}} \\ $$$${and}\:{y}\:=\:{cos}^{\mathrm{2}} \:\frac{\pi}{\mathrm{5}}+{cos}^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{15}}+{cos}^{\mathrm{2}} \frac{\mathrm{8}\pi}{\mathrm{15}}. \\ $$$${find}\:{x}+{y}\:? \\ $$…

If-4sinx-cosy-2sinx-2cosy-1-0-where-x-y-0-2pie-Find-largest-possible-value-of-the-sum-x-y-

Question Number 29491 by math solver last updated on 09/Feb/18 $${If}\:\mathrm{4}{sinx}.{cosy}+\mathrm{2}{sinx}+\mathrm{2}{cosy}+\mathrm{1}=\mathrm{0} \\ $$$${where}\:{x},{y}\:\in\:\left[\mathrm{0},\mathrm{2}{pie}\right].\:{Find}\:{largest}\: \\ $$$${possible}\:{value}\:{of}\:{the}\:{sum}\:\left({x}+{y}\right). \\ $$ Answered by ajfour last updated on 09/Feb/18 $$\left(\mathrm{1}+\mathrm{2sin}\:{x}\right)\left(\mathrm{1}+\mathrm{2cos}\:{y}\right)=\mathrm{0}…

the-number-of-ordered-pairs-x-y-of-real-numbers-satisfying-4x-2-4x-2-sin-2-y-and-x-2-y-2-3-is-

Question Number 29478 by math solver last updated on 09/Feb/18 $${the}\:{number}\:{of}\:{ordered}\:{pairs}\:\left({x},{y}\right) \\ $$$${of}\:{real}\:{numbers}\:{satisfying}\: \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{2}={sin}^{\mathrm{2}} {y} \\ $$$${and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\:\mathrm{3}\:{is}\:? \\ $$ Answered by…