If $\sin(x)=3\cos(x)$, compute $\sin(x)*\cos(x)$ I drew a triangle and was instructed to use a property unknown to me. Apparently the answer is $\frac{3}{\sqrt{10}}*\frac{1}{\sqrt{10}}=\frac{3}{10}$. Is this answer correct, and what theorem/formula is this?

$$\begin{align} \\
\sin (2x)&=2\sin (x)\cos (x) \\
&=\frac {2\tan (x)}{1+\tan^2 (x)} \\
&=\frac {2\cdot3}{1+(3)^2} \\
&=\frac {6}{10} \\
\end{align}$$
thus
$$\sin (x)\cos (x)=\frac {3}{10}$$
