1)
[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)
\\\\\\
cos(\theta )=\sqrt{1-sin^2(\theta )}\\\\
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sin(x)=cos(x)-1\implies sin(x)=\sqrt{1-sin^2(x)}-1[/tex]
[tex]\bf sin(x)+1=\sqrt{1-sin^2(x)}\implies [sin(x)+1]^2=1-sin^2(x)
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sin^2(x)+2sin(x)+1=1-sin^2(x)\implies 2sin^2(x)+2sin(x)=0
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2sin(x)[sin(x)+1]=0\implies
\begin{cases}
2sin(x)=0\\
sin(x)=0\\
\measuredangle x=0~,~\pi ~,~2\pi \\
-------\\
sin(x)+1=0\\
sin(x)=-1\\
\measuredangle x=\frac{3\pi }{2}
\end{cases}[/tex]
2)
[tex]\bf 3sin(x)+cos^2(x)=2
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3sin(x)+[1-sin^2(x)]=2
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3sin(x)-sin^2(x)+1=2
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3sin(x)-sin^2(x)-1=0
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sin^2(x)-3sin(x)+1=0
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\boxed{[sin(x)-3][sin(x)+1]=0}\impliedby \textit{check closely this }FOIL[/tex]
