Use sin(2t)=2sin(t)cos(t) to rewrite sin(6x)cos(6x).

Question

Use sin(2t)=2sin(t)cos(t) to rewrite sin(6x)cos(6x).

sin(6x)cos(6x)=

A.1/2sin(3x)

B. 2sin(3x)

C. 2sin(12x)

Answer 1

Since sin(2t) = 2 sin(t)cos(t), it basically means that if you divided the argument (stuff in parentheses) of sine by 2, you make that the new argument of sine and cosine multiplied together, times 2. For example:

sin(4t) = 2 sin(2t)cos(2t)

sin (10t) = 2 sin(5t)cos(5t)

So for this problem, since we want to end up with an argument of 6x, that means we need to have an original argument of 12x. But we don't have a coefficient of 2 on our original sin(6x)cos(6x), so that means we need to multiply our sine by 1/2 to get that to cancel.

Final answer : 1/2 sin (12x)

Check: 1/2 [ 2 sin(6x)cos(6x) ]

sin(6x)cos(6x)