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If $\sin \theta+\cos \theta=1$, then $\sin \theta \cos \theta=$
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$\sin \theta+\cos \theta=1$
Squaring on both sides, we get
$\begin{aligned}
& \Rightarrow \sin ^2 \theta+\cos ^2 \theta+2 \sin \theta \cos \theta=1 \\
& \therefore \sin \theta \cos \theta=0 .
\end{aligned}$
Squaring on both sides, we get
$\begin{aligned}
& \Rightarrow \sin ^2 \theta+\cos ^2 \theta+2 \sin \theta \cos \theta=1 \\
& \therefore \sin \theta \cos \theta=0 .
\end{aligned}$
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