Finding solutions using trigonometric identities I have an exam tomorrow and it is highly likely that there will be a trig identity on it. To practice I tried this identity:
$$2 \sin 5x\cos 4x-\sin x = \sin9x$$
We solved the identity but we had to move terms from one side to another. 
My question is: what are the things that you can and cannot do with trig identities? 
And what things are must not when doing trig identities?
Thank you

$$\sin C+\sin D=2\sin\frac{C+D}2\cos\frac{C-D}2$$
So, $$\sin9x+\sin x=2\sin\frac{9x+x}2\cos\frac{9x-x}2=2\sin5x\cos4x$$

$$2\sin A\cos B=\sin(A+B)+\sin(A-B)$$
So, $$2\sin5x\cos4x=\sin(5x+4x)+\sin(5x-4x)=\sin9x+\sin x$$
