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Question Number 93256 by i jagooll last updated on 12/May/20

$$\{\begin{array}{l}3\cos \mathrm{x}=4\cos \mathrm{y}\\ 3\sin \mathrm{x}+4\sin \mathrm{y}=5\end{array}$$ $$\mathrm{find}\mathrm{x}\mathrm{\&}\mathrm{y}\mathrm{with}\mathrm{acute}\mathrm{angle}$$

Commented byjohn santu last updated on 12/May/20

$$\{\begin{array}{l}9\cos {}^2\mathrm{x}=16\cos {}^2\mathrm{y}\\ 9\sin {}^2\mathrm{x}=25-40\sin \mathrm{y}+16\sin {}^2\mathrm{y}\end{array}$$ $$\mathrm{add}\left(1\right)\mathrm{and}\left(2\right)$$ $$9=41-40\sin \mathrm{y}$$ $$\sin \mathrm{y}=\frac{4}{5}\Rightarrow \mathrm{y}\approx 53.{13}^{\mathrm{o}}$$ $$\Rightarrow 3\sin \mathrm{x}+4\sin \mathrm{y}=5$$ $$3\sin \mathrm{x}=5-\frac{16}{5}=\frac{9}{5}$$ $$\sin \mathrm{x}=\frac{3}{5}\Rightarrow \mathrm{x}={\sin }^{-1}\left(\frac{3}{5}\right)$$ $$\mathrm{x}\approx 36.{86}^{\mathrm{o}}$$

Commented byi jagooll last updated on 12/May/20

thank you sir. cooll man ������

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