Proving Sin 6x Cos 4x + Cos 4x sin 2x = Cos 2x tan 8x

[texas_kiwi]

I am trying to prove this equation:

Sin 6x Cos 4x + Cos 4x sin 2x =

Cos 2x tan 8x​

Tan 8x​

does anyone have any idea??

 

[courtrigrad]

$$\sin 6x\cos 4x = \frac{1}{2}(\sin 10x + \sin 2x)$$
$$\cos 4x\sin 2x = \frac{1}{2}(\sin 6x - \sin 2x)$$.

So we get $$\frac{1}{2}(\sin 10x + \sin 6x)$$

or $$\sin 8x\cos 2x$$.

The second expression is not right. Just plug in some values.

 

[ريمان]

yes I will tray to slove it

before some month I one like this and I see new law
tan(a)+tan(b)
tab(a)-tan(b)

I discoverd new law juist in my opinion