\(\operatorname{tg}{\alpha}\) - ро ёбед, агар \(2\operatorname{tg}{\alpha}-\sin{\alpha}+5\cos{\alpha}=10.\)
\(2\operatorname{tg}{\alpha}-\sin{\alpha}+5\cos{\alpha}=10,\)
\(2\operatorname{tg}{\alpha}-\sin{\alpha}+5\cos{\alpha}-10=0\)
\(\operatorname{tg}{\alpha}=\frac{\sin{\alpha}}{\cos{\alpha}}\)
\(5\cos{\alpha}-\sin{\alpha}+2\cdot\frac{\sin{\alpha}}{\cos{\alpha}}-10=0\)
\(5\cos{\alpha}-\sin{\alpha}-2\cdot(5-\frac{\sin{\alpha}}{\cos{\alpha}})=0\)
\((5\cos{\alpha}-\sin{\alpha}-2\cdot(5-\frac{\sin{\alpha}}{\cos{\alpha}}))\cdot\cos{\alpha}=0\cdot\cos{\alpha}\)
\(\cos{\alpha}\cdot(5\cos{\alpha}-\sin{\alpha})-2\cdot(5\cos{\alpha}-sin{\alpha})=0\)
\((5\cos{\alpha}-\sin{\alpha})\cdot(\cos{\alpha}-2)=0\)
\(\cos{\alpha}-2\neq0\)
\(5\cos{\alpha}-\sin{\alpha}=0\)
\(2\operatorname{tg}{\alpha}-\sin{\alpha}+5\cos{\alpha}=10\)
\(2\operatorname{tg}{\alpha}=10\)
\(\operatorname{tg}{\alpha}=5\)
Ҷавоб: 5