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 co...--prophetes.ai

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?

We have $\tan(x) = 3$

Draw a right angle triangle where $x$ is one of the angle, let the opposite side be of length $3$, let the adjacent side be of length one. Then by Pythagoras Theorem, the hypothenus side is $\sqrt{10}$.

Hence you can compute $\sin(x)$ and $\cos(x)$ and multiply them.

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?

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?