Question

cos5x*cos8x

Answer 1

$cos5x*cos8x= 1/2 (cos⁡(-3x)+cos13x)=cos⁡(-3x/2)+cos 13x/2$

Answer 2

cos(5x) * cos(8x) can be simplified using the trigonometric identity:

cos(a) * cos(b) = 1/2 * (cos(a + b) + cos(a - b))

So, applying this identity to cos(5x) * cos(8x), we get:

1/2 * (cos(5x + 8x) + cos(5x - 8x)) = 1/2 * (cos(13x) + cos(-3x))

Since cos(-x) = cos(x), we can simplify further:

1/2 * (cos(13x) + cos(3x))

So, the simplified form of cos(5x) * cos(8x) is 1/2 * (cos(13x) + cos(3x).