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Question Number 106950 by bemath last updated on 08/Aug/20

$${}^{@bemath@}$$$$Given\{\begin{array}{l}2\cos x+7\cos y=5\\ 2\sin x+7\sin y=6\end{array}$$$$\cos (x-y)=?$$

Answered by john santu last updated on 08/Aug/20

$$⧫\mathrm{JS}◊$$$$\to \{\begin{array}{l}4\cos {}^2\mathrm{x}+14\cos \mathrm{xcos}\mathrm{y}+49\cos {}^2\mathrm{y}=25\\ 4\sin {}^2\mathrm{x}+14\sin \mathrm{xsin}\mathrm{y}+49\sin {}^2\mathrm{y}=36\end{array}$$$$\left(1\right)+\left(2\right)\Rightarrow 53+14\cos (\mathrm{x}-\mathrm{y})=61$$$$\cos (\mathrm{x}-\mathrm{y})=\frac{61-53}{14}=\frac{8}{14}=\frac{4}{7}$$

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