Question

1) Giai phuong trinh:

a) 2cos²2x + 3sin²x = 2

Answer 1

\(\Leftrightarrow2cos^22x+3\left(\dfrac{1}{2}-\dfrac{1}{2}cos2x\right)=2\)

\(\Leftrightarrow4cos^22x-3cos2x-1=0\)

\(\Rightarrow\left[{}\begin{matrix}cos2x=1\\cos2x=-\dfrac{1}{4}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=k2\pi\\2x=\pm arccos\left(-\dfrac{1}{4}\right)+k2\pi\\\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=k\pi\\x=\pm\dfrac{1}{2}arccos\left(-\dfrac{1}{4}\right)+k\pi\end{matrix}\right.\)