Răspuns:
Răspuns:
[tex]\frac{5sinx+7cosx}{6cosx-3sinx}=? \\[/tex]
[tex]tgx=\frac{sinx}{cosx}=\frac{4}{15}[/tex]
Voi face separat 5sinx+7cosx si 6cosx-3sinx apoi voi inlocui in ecuatie:
[tex]5sinx+7cosx=cosx(5*\frac{sinx}{cosx} +7)=cosx(5*tgx+7)[/tex]
[tex]6cosx-3sinx=cosx(6-3*\frac{sinx}{cosx})=cosx(6-3*tgx)[/tex]
Inlocuim:
[tex]\frac{cosx(5*tgx+7)}{cosx(6-3*tgx)}=\frac{5*\frac{4}{15}+7 }{6-3*\frac{4}{15} }=\frac{\frac{4}{3}+\frac{21}{3} }{\frac{30}{5}-\frac{4}{5} }=\frac{\frac{25}{3} }{\frac{26}{5} }=\frac{125}{78}[/tex]
