Question

найдите значение tgx, если
(2sinx-cosx)/(2cosx+sinx)=3

Answer 1

$\frac{2sinx-cosx}{2cosx+sinx}=3\\\\\frac{\frac{2sinx}{cos x}-\frac{cosx}{cosx}}{\frac{2cosx}{cosx}+\frac{sinx}{cosx}}=3\\\\\frac{2tgx-1}{2+tgx}=3\\\\3(2+tgx)=2tgx-1\\\\6+3tgx=2tgx-1\\\\3tgx-2tgx=-1-6\\\\tgx=-7$