اوجد المدى

19sin^2(x)+10cos^2(x)+10

$\large {\color{Red} y=19sin^{2}x+10cos^{2}x+10=19sin^{2}x+10-10sin^{2}x+10}$
${\color{DarkBlue} y=9sin^{2}x+20\rightarrow 9sin^{2}x=y-20\rightarrow sin^{2}x=\frac{y-20}{9}}$
${\color{Blue} 0\leq sin^{2}x\leq 1\Rightarrow 0\leq \frac{y-20}{9}\leq 1\Rightarrow 20\leq y\leq 29 }$
${\color{DarkBlue} Rang=[20,29]}$