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Question Number 172189 by Mikenice last updated on 23/Jun/22 Answered by Mathspace last updated on 24/Jun/22 $${let}\:{u}_{{n}} =\prod_{{k}=\mathrm{1}} ^{{n}} \left(\varphi\left({a}+\frac{{kb}}{{n}}\right)\right)^{\frac{\mathrm{1}}{{n}}} \\ $$$$\Rightarrow{lim}_{{n}\rightarrow+\infty} {ln}\left({u}_{{n}} \right) \\…
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Question Number 106579 by john santu last updated on 06/Aug/20 $$\mathcal{G}\mathrm{iven}\:\mathrm{cos}\:\mathrm{x}+\mathrm{cos}\:\mathrm{y}=\frac{\mathrm{3}}{\mathrm{2}}+\mathrm{cos}\:\left(\mathrm{x}+\mathrm{y}\right) \\ $$$$\mathrm{where}\:\mathrm{x},\mathrm{y}\:\in\:\left[\mathrm{0},\mathrm{2}\pi\:\right].\:\mathrm{find}\:\mathrm{x}\:\&\:\mathrm{y}\: \\ $$ Answered by bobhans last updated on 06/Aug/20 $$\mathrm{cos}\:\mathrm{x}+\mathrm{cos}\:\mathrm{y}\:=\:\frac{\mathrm{3}}{\mathrm{2}}+\mathrm{cos}\:\mathrm{xcos}\:\mathrm{y}−\mathrm{sin}\:\mathrm{xsin}\:\mathrm{y} \\ $$$$\mathrm{cos}\:\mathrm{x}+\mathrm{cos}\:\mathrm{y}−\mathrm{cos}\:\mathrm{xcos}\:\mathrm{y}+\mathrm{sin}\:\mathrm{xsin}\:\mathrm{y}=\frac{\mathrm{3}}{\mathrm{2}}…
Question Number 172026 by Mikenice last updated on 23/Jun/22 $${show}\:{that} \\ $$$${sin}^{\mathrm{2}} \alpha+\left(\mathrm{1}+{cos}\alpha\right)^{\mathrm{2}} =\mathrm{2}\left(\mathrm{1}+{cos}\alpha\right) \\ $$ Answered by puissant last updated on 23/Jun/22 $${sin}^{\mathrm{2}} \alpha+\left(\mathrm{1}+{cos}\alpha\right)^{\mathrm{2}}…
Question Number 106468 by bemath last updated on 05/Aug/20 $$\mathrm{4cos}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{3x}\:=\:\mathrm{1} \\ $$ Answered by john santu last updated on 05/Aug/20 $$\mathrm{recall}\::\:\mathrm{2cos}\:\mathrm{3x}\:\mathrm{cos}\:\mathrm{x}\:=\:\mathrm{cos}\:\mathrm{4x}+\mathrm{cos}\:\mathrm{2x} \\ $$$$\Rightarrow\mathrm{2}\left\{\mathrm{cos}\:\mathrm{4x}+\mathrm{cos}\:\mathrm{2x}\right\}\mathrm{cos}\:\mathrm{2x}=\mathrm{1} \\ $$$$\mathrm{2}\left\{\mathrm{2cos}\:^{\mathrm{2}}…
Question Number 172000 by Mikenice last updated on 23/Jun/22 $${prove}\:{that}: \\ $$$$\frac{{sinx}}{{sin}\mathrm{3}{x}}+\frac{{tanx}}{{tan}\mathrm{3}{x}}=\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 40906 by Penguin last updated on 29/Jul/18 $${f}\left({x}\right)\:=\:\mathrm{5}.\mathrm{687cosh}\left(\frac{{x}}{\mathrm{5}.\mathrm{687}}\right)−\mathrm{5}.\mathrm{687} \\ $$$${L}=\int_{-\mathrm{11}} ^{\mathrm{11}} \sqrt{\mathrm{1}+\left[{f}\:'\left({x}\right)\right]^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 40875 by Tawa1 last updated on 28/Jul/18 $$\mathrm{2a}\:\mathrm{sin}\left(\frac{\mathrm{25}}{\mathrm{a}}\right)\:−\:\mathrm{51}\:=\:\mathrm{0},\:\:\mathrm{find}\:\mathrm{a} \\ $$ Answered by MrW3 last updated on 29/Jul/18 $${let}'{s}\:{have}\:{a}\:{look}\:{at}\:{the}\:{function}\:{f}\left({x}\right)=\frac{\mathrm{sin}\:\left({x}\right)}{{x}}. \\ $$$${we}\:{know}\:{following}\:{about}\:{it}: \\ $$$${f}\left(−{x}\right)={f}\left({x}\right)\:\Rightarrow{symmetric} \\…