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If $\sin\theta + \cos\theta = \sqrt{3}$, then find the value of $\sin\theta \cdot \cos\theta$ .
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$\sin \theta + \cos \theta = \sqrt{3}$
squaring both sides
$\sin^2 \theta + \cos^2 \theta + 2 \sin\theta \cos \theta = 3$
$\Rightarrow 1 + 2 \sin \theta \cos \theta = 3$
$\Rightarrow \sin \theta \cos \theta = 1$
squaring both sides
$\sin^2 \theta + \cos^2 \theta + 2 \sin\theta \cos \theta = 3$
$\Rightarrow 1 + 2 \sin \theta \cos \theta = 3$
$\Rightarrow \sin \theta \cos \theta = 1$