\(2\cdot sin2x+1=0\)
=>\(2\cdot sin2x=-1\)
=>\(sin2x=-\dfrac{1}{2}\)
=>\(\left[{}\begin{matrix}2x=-\dfrac{\Omega}{6}+k2\Omega\\2x=\Omega+\dfrac{\Omega}{6}+k2\Omega=\dfrac{7}{6}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-\dfrac{\Omega}{12}+k2\Omega=-15^0+k\cdot360^0\\x=\dfrac{7}{12}\Omega+k2\Omega=105^0+k\cdot360^0\end{matrix}\right.\)
\(0< x< 90^0\)
=>\(\left[{}\begin{matrix}0< -15^0+k\cdot360^0< 90^0\\0< 105^0+k\cdot360^0< 90^0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}15^0< k\cdot360^0< 105^0\\-105^0< k\cdot360^0< -15^0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{12}< k< \dfrac{7}{24}\\-\dfrac{7}{24}< k< -\dfrac{1}{12}\end{matrix}\right.\)
mà k nguyên
nên \(k\in\varnothing\)
=>\(x\in\varnothing\)
