Answer
$x=\{0.3630,2.1351\}$
Work Step by Step
$cos(x)+3sin(x)-2=0$
$[3sin(x)-2]^2=[-cos(x)]^2$
$9sin^2(x)-12sin(x)+4=cos^2(x)$
$9sin^2(x)-12sin(x)+4-cos^2(x)=0$
$9sin^2(x)-12sin(x)+4-[1-sin^2(x)]=0$
$9sin^2(x)-12sin(x)+4-1+sin^2(x)=0$
$10sin^2(x)-12sin(x)+3=0$
$sin(x)=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-12) \pm \sqrt{(-12)^2 - 4 (10)(3)}}{2(10)}=\frac{6+\sqrt{6}}{10},\frac{6-\sqrt{6}}{10}$
$sin(x)=\frac{6-\sqrt{6}}{10}=0.355$
$x=sin^{-1}(\frac{6-\sqrt{6}}{10})$
$x=0.3630$
$sin(x)=\frac{6-\sqrt{6}}{10}=0.845\;\;\;\;$
$x=sin^{-1}(\frac{6-\sqrt{6}}{10})$
$x=2.1351$
$x=\{0.3630,2.1351\}$
