Обчисліть 4sinL-cosL/cosL+4sinLЯкщо ctgL=1/3. Created by krakb17. algebra-ru

Первый способ :Второй способ :

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l6987106

Первый способ :

$\frac{4Sin\alpha-Cos\alpha}{Cos\alpha+4Sin\alpha} =\frac{\frac{4Sin\alpha}{Sin\alpha}-\frac{Cos\alpha}{Sin\alpha}}{\frac{Cos\alpha}{Sin\alpha}+\frac{4Sin\alpha}{Sin\alpha}}=\frac{4-Ctg\alpha}{Ctg\alpha+4}=\frac{4-\frac{1}{3}}{\frac{1}{3}+4}=\frac{3\frac{2}{3}}{4\frac{1}{3}}=\frac{11}{3}*\frac{3}{13}=\frac{11}{13}$

Второй способ :

$Ctg\alpha =\frac{1}{3}\\\\\frac{Cos\alpha}{Sin\alpha}=\frac{1}{3} \Rightarrow Sin\alpha=3Cos\alpha\\\\\frac{4Sin\alpha-Cos\alpha}{Cos\alpha+4Sin\alpha}=\frac{4*3Cos\alpha-Cos\alpha}{Cos\alpha+4*3Cos\alpha}=\frac{11Cos\alpha}{13Cos\alpha}=\frac{11}{13}$

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Объяснение:

https://ru-static.z-dn.net/files/db8/e6fb6e4261fad8dce6abe4e01039089b.jpg

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