\(\Leftrightarrow\sqrt{\left(2\sqrt{3}\right)^2+1^2}\cdot\sin\left(x+\alpha\right)=\dfrac{9}{2}\)
\(\Leftrightarrow\sqrt{7}\cdot\sin\left(x+\alpha\right)=\dfrac{9}{2}\)
\(\cos a=\dfrac{2\sqrt{3}}{\sqrt{7}}=\dfrac{2\sqrt{21}}{7};\sin a=\dfrac{1}{\sqrt{7}}=\dfrac{\sqrt{7}}{7}\)
\(\Leftrightarrow\sin\left(x+\alpha\right)=\dfrac{9}{2\sqrt{7}}>1\)
=>PTVN
\(cosx+2\sqrt{3}sinx=\dfrac{9}{2}\Leftrightarrow2cosx+4\sqrt{3}sinx=9\)
\(\Leftrightarrow\dfrac{2}{\sqrt{2^2+\left(4\sqrt{3}\right)^2}}cosx+\dfrac{4\sqrt{3}}{\sqrt{2^2+\left(4\sqrt{3}\right)^2}}sinx=\dfrac{9}{\sqrt{2^2+\left(4\sqrt{3}\right)^2}}\)
\(\Leftrightarrow\dfrac{\sqrt{13}}{13}cosx+\dfrac{2\sqrt{39}}{13}sinx=\dfrac{9\sqrt{13}}{26}\)
\(\Leftrightarrow sin\left(16^o\right).cosx+cos\left(16^o\right).sinx=\dfrac{9\sqrt{13}}{26}\)
\(\Leftrightarrow sin\left(16^o+x\right)=\dfrac{9\sqrt{13}}{26}\)
\(\Rightarrow VN\)
