Pt\(\Leftrightarrow sinx+cosx+2sinx.cosx-1=0\)
Đặt \(t=sinx+cosx;t\in\left[-\sqrt{2};\sqrt{2}\right]\)
\(\Rightarrow t^2-1=2sinx.cosx\)
Pttt:\(t+t^2-1-1=0\)
\(\Leftrightarrow t^2+t-2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}t=1\left(tm\right)\\t=-2\left(ktm\right)\end{matrix}\right.\)
\(\Rightarrow sinx+cosx=1\Leftrightarrow sin\left(x+\dfrac{\pi}{4}\right)=\dfrac{1}{\sqrt{2}}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\dfrac{\pi}{2}+k\pi2\end{matrix}\right.\)\(\left(k\in Z\right)\)
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