Question

6 sin альфа -4 cos альфа /4 sin альфа -10 cos альфа =-1

Answer 1

$\frac{6Sin\alpha-4Cos\alpha}{4Sin\alpha-10Cos\alpha}=-1\\\\6Sin\alpha-4Cos\alpha=-4Sin\alpha+10Cos\alpha\\\\6Sin\alpha-4Cos\alpha+4Sin\alpha-10Cos\alpha=0\\\\10Sin\alpha -14Cos\alpha=0\\\\5Sin\alpha -7Cos\alpha=0|:Cos\alpha\neq0\\\\5tg\alpha-7=0\\\\tg\alpha=\frac{7}{5} \\\\\alpha=arctg\frac{7}{5}+\pi n,n \in Z\\\\\alpha=arctg1,4+\pi n,n\in Z$