Question

Is `6sin(x)cos(x)` equivalent to `3sin(2x)` or `sin(3x)`?

Answer 1

The usual identity is:

`sin 2 x = 2 sin x cos x`

Therefore:

`alpha sin 2 x = 2alpha sin x cos x`

Or, reversing the order:

`2alpha sin x cos x = alpha sin 2 x`

With `alpha = 3`, that becomes:

`6 sin x cos x= 3 sin 2 x`