Найти tga если (3sina-5cosa+2)/(sina+3cosa+6)=1/3

3sina-5cosa+2sina+3cosa+6=13 => 9sina-15cosa+6=sina+3cosa+6 => 8sina=18cosa => sinacosa=188=94=2,25 => tga=2,25

[latex]\frac{3sin a-5cos a+2}{sin a+3cos a+6}=\frac{1}{3}[/latex] [latex]3(3sin a-5cos a+2)=1*(sin a+3cos a+6)[/latex] [latex]9sin a-15cos a+6=sin a+3cos a+6[/latex] [latex]9sin a-15cos a=sin a+3cos a[/latex] [latex]9sin a-sin a=3cos a+15cosa[/latex] [latex]8 sin a=18 cos a[/latex] [latex]tg a=\frac{18}{8}=2.25[/latex] [latex]tg a=2.25[/latex]