write 5 cos 3x cos 2x as a sum or difference of trigonometric functions

Question

write 5 cos 3x cos 2x as a sum or difference of trigonometric functions

Answer 1

A suitable identity for this problem is:

2 cos a cos b = cos (a + b) + cos (a - b).

Evidently, one possible mapping of variables is:

a = 3x, b = 2x

So we get:

(5 / 2) (2 / 5) 2 cos 3x cos 2x = cos (3x + 2x) + cos (3x - 2x)

(2 / 2) (2 / 5) 5 cos 3x cos 2x = cos 5x + cos x

5 cos 3x cos 2x = (5 / 2) (cos 5x + cos x)

Answer 2

(-2√10 - 2)/9 or -2(√10 - 1)/9