If $\sin heta + \cos heta = \sqrt{3}$, then find the value of $\sin heta \cdot \cos heta$.

Question

If $\sin 	heta + \cos 	heta = \sqrt{3}$, then find the value of $\sin 	heta \cdot \cos 	heta$.

Accepted Answer

Step 1: $\sin 	heta + \cos 	heta = \sqrt{3}$
Squaring both sides:
$\sin^2 	heta + \cos^2 	heta + 2 \sin 	heta \cos 	heta = 3$
Step 2: $\Rightarrow 1 + 2 \sin 	heta \cos 	heta = 3$
Step 3: $\Rightarrow \sin 	heta \cos 	heta = 1$

Question

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