a, \(sin\left(2x+45^o\right)=-\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+45^o=-30^o+k.360^o\\2x+45^o=-150^o+k.360^o\end{matrix}\right.\)
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b, \(cos\left(4x+\dfrac{\pi}{5}\right)-sin2x=0\)
\(\Leftrightarrow cos\left(4x+\dfrac{\pi}{5}\right)-cos\left(\dfrac{\pi}{2}-2x\right)=0\)
\(\Leftrightarrow-2sin\left(x+\dfrac{\pi}{20}\right).sin\left(3x-\dfrac{3\pi}{20}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\left(x+\dfrac{\pi}{20}\right)=0\\sin\left(3x-\dfrac{3\pi}{20}\right)=0\end{matrix}\right.\)
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c, \(sin^22x-cos2x+1=0\)
\(\Leftrightarrow cos^22x+cos2x-2=0\)
\(\Leftrightarrow\left(cosx-1\right)\left(cosx+2\right)=0\)
\(\Leftrightarrow cosx=1\)
\(\Leftrightarrow x=k2\pi\)