Category: Trigonometry

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Question Number 106579 by john santu last updated on 06/Aug/20 $$\mathcal{G}\mathrm{iven}\cos \mathrm{x}+\cos \mathrm{y}=\frac{3}{2}+\cos (\mathrm{x}+\mathrm{y})$$$$\mathrm{where}\mathrm{x},\mathrm{y}\in [0,2\pi ].\mathrm{find}\mathrm{x}\mathrm{\&}\mathrm{y}$$ Answered by bobhans last updated on 06/Aug/20 $$\cos \mathrm{x}+\cos \mathrm{y}=\frac{3}{2}+\cos \mathrm{xcos}\mathrm{y}-\sin \mathrm{xsin}\mathrm{y}$$$$\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 106468 by bemath last updated on 05/Aug/20 $$4\cos \mathrm{x}\cos 2\mathrm{x}\cos 3\mathrm{x}=1$$ Answered by john santu last updated on 05/Aug/20 $$\mathrm{recall}:2\cos 3\mathrm{x}\cos \mathrm{x}=\cos 4\mathrm{x}+\cos 2\mathrm{x}$$$$\Rightarrow 2\{\cos 4\mathrm{x}+\cos 2\mathrm{x}\}\cos 2\mathrm{x}=1$$$$\mathrm{2}\left\{\mathrm{2cos}\:^{\mathrm{2}}…

Question Number 40906 by Penguin last updated on 29/Jul/18 $$f\left(x\right)=5.687\cosh \left(\frac{x}{5.687}\right)-5.687$$$$L={\int }_{-11}^{11}\sqrt{1+{\left[f{}^{\prime }\left(x\right)\right]}^2}dx$$ Commented by maxmathsup by imad last updated on…