Question

verify the identity sin theta + sin 3 theta/ cos theta + cos 3 theta = tan 2 theta

Answer 1

\[\frac{\sin \theta +\sin 3\theta}{\cos \theta+\cos 3\theta}=\tan 2\theta \]

Answer 2

\[\sin3 \theta+\sin \theta=2\sin \frac{3\theta+\theta}{2}\cos \frac{3\theta-\theta}{2}\]

Answer 3

i got that

Answer 4

but when i went to simplify i nee to get rid of the 2 in
front of the sin and cos

Answer 5

Use that and also this:
\[\cos 3\theta+\cos \theta =2\cos \frac{3\theta+\theta}{2}\cos \frac{3\theta-\theta}{2}\]

Answer 6

\[\frac{2\sin 2\theta \cos \theta}{2\cos 2\theta \cos \theta}=\tan 2\]

Answer 7

tan 2 theta that is

Answer 8

You follow?