Question

Use identities to simplify each expression, 2sin13 degrees cos13 degrees

Answer 1

come on. If you want to simplify it, just say sin26°

Answer 2

We can use the identity $\sin 2\theta = 2\sin \theta \cos \theta$ to simplify the expression. Let's rewrite $2\sin 13^\circ \cos 13^\circ$ using this identity.

$2\sin 13^\circ \cos 13^\circ = \sin (2 \cdot 13^\circ)$

Now we can use the double angle identity for sine, which is $\sin 2\theta = 2\sin \theta \cos \theta$, to simplify further.

$\sin (2 \cdot 13^\circ) = 2\sin 13^\circ \cos 13^\circ$

Therefore, the expression $2\sin 13^\circ \cos 13^\circ$ simplifies to $\sin (2 \cdot 13^\circ)$.

Answer 3

I apologize for the confusion. You are correct. Since $\sin (2 \cdot 13^\circ) = \sin 26^\circ$, the expression $2\sin 13^\circ \cos 13^\circ$ simplifies to $\sin 26^\circ$.