Đáp án:
\(\left[ \begin{array}{l}x=k.\pi\\x=arctan 2+k.\pi\end{array} \right.\) \((k \epsilon Z)\)
Giải thích các bước giải:
\(\sin^{2} x+\sin 2x+2\cos^{2} x=2\)
\(\Leftrightarrow \sin^{2} x+\sin 2x=2(1-\cos^{2} x)\)
\(\Leftrightarrow \sin^{2} x+\sin 2x -2\sin^{2} x=0\)
\(\Leftrightarrow -\sin^{2} x+\sin 2x=0\)
\(\Leftrightarrow 2\sin x \cos x-\sin^{2} x=0\)
\(\Leftrightarrow \sin x(2\cos x-\sin x)=0\)
\(\Leftrightarrow \) \(\left[ \begin{array}{l}\sin x=0\\2\cos x-\sin x=0\end{array} \right.\)
\(\Leftrightarrow \) \(\left[ \begin{array}{l}x=k.\pi\\\tan x=2\end{array} \right.\)
\(\Leftrightarrow \) \(\left[ \begin{array}{l}x=k.\pi\\x=arctan 2+k.\pi\end{array} \right.\) \((k \epsilon Z)\)
