ĐK: \(x\ne45^o+k.180^o\)
\(tan\left(x+45^o\right)=1+sin2x\)
\(\Leftrightarrow\dfrac{sin\left(x+45^o\right)}{cos\left(x+45^o\right)}=\left(sinx+cosx\right)^2\)
\(\Leftrightarrow\dfrac{sin\left(x+45^o\right)}{cos\left(x+45^o\right)}=2sin^2\left(x+45^o\right)\)
\(\Leftrightarrow sin\left(x+45^o\right)\left[\dfrac{1}{cos\left(x+45^o\right)}-2sin\left(x+45^o\right)\right]=0\)
\(\Leftrightarrow sin\left(x+45^o\right)\left[1-2sin\left(x+45^o\right).cos\left(x+45^o\right)\right]=0\)
\(\Leftrightarrow sin\left(x+45^o\right)\left[1-sin\left(2x+90^o\right)\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\left(x+45^o\right)=0\\sin\left(2x+90^o\right)=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+45^o=k.180^o\\2x+90^o=90^o+k.360^o\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-45^o+k.180^o\\x=k.180^o\end{matrix}\right.\)
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