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\(\operatorname{tg}{\alpha}\) - ро ёбед, агар \(2\operatorname{tg}{\alpha}-\sin{\alpha}+5\cos{\alpha}=10.\)

\(2\operatorname{tg}{\alpha}-\sin{\alpha}+5\cos{\alpha}=10,\)

\(2\operatorname{tg}{\alpha}-\sin{\alpha}+5\cos{\alpha}-10=0\)

\(\operatorname{tg}{\alpha}=\frac{\sin{\alpha}}{\cos{\alpha}}\)

\(5\cos{\alpha}-\sin{\alpha}+2\cdot\frac{\sin{\alpha}}{\cos{\alpha}}-10=0\)

\(5\cos{\alpha}-\sin{\alpha}-2\cdot(5-\frac{\sin{\alpha}}{\cos{\alpha}})=0\)

\((5\cos{\alpha}-\sin{\alpha}-2\cdot(5-\frac{\sin{\alpha}}{\cos{\alpha}}))\cdot\cos{\alpha}=0\cdot\cos{\alpha}\)

\(\cos{\alpha}\cdot(5\cos{\alpha}-\sin{\alpha})-2\cdot(5\cos{\alpha}-sin{\alpha})=0\)

\((5\cos{\alpha}-\sin{\alpha})\cdot(\cos{\alpha}-2)=0\)

\(\cos{\alpha}-2\neq0\)

\(5\cos{\alpha}-\sin{\alpha}=0\)

\(2\operatorname{tg}{\alpha}-\sin{\alpha}+5\cos{\alpha}=10\)

\(2\operatorname{tg}{\alpha}=10\)

\(\operatorname{tg}{\alpha}=5\)

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