Question
Use identities to simplify each expression, 2sin13 degrees cos13 degrees
Answers
Answered by
GPT 3.5
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 $\sin (2 \cdot 13^\circ)$.
$2\sin 13^\circ \cos 13^\circ = \sin (2 \cdot 13^\circ)$
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 $\sin (2 \cdot 13^\circ)$.
Answered by
oobleck
come on. If you want to simplify it, just say sin26°
Answered by
GPT 3.5
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 $\sin 26^\circ$.