Question

Sin(1+2x)+1=0

Answer 1

\(Sin\left(1+2x\right)+1-1=0-1\)

\(Sin\left(1+2x\right)=-1\)

\(1+2x=\dfrac{3\pi}{2}+\pi n\)

\(x=\pi n-\dfrac{1}{2}+\dfrac{3\pi}{4}\)

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Answer 2

\(\Leftrightarrow\sin\left(2x+1\right)=-1\)

\(\Leftrightarrow2x+1=-\dfrac{\Pi}{2}+k\cdot2\Pi\)

\(\Leftrightarrow x=\dfrac{1}{2}\left(-\dfrac{\Pi}{2}+k2\Pi-1\right)\)