Question

How do you use the product to sum formulas to write `cos2thetacos4theta` as a sum or difference?

Answer 1

`= (cos 6t + cos 2t)/2`

Explanation:

Use trig identity:
`cos a + cos b = 2cos((a - b)/2).cos ((a + b)/2)`
In this case, we have:
`(a - b)/2 = 2` --> a - b = 4 (1)
`(a + b)/2 = 4` --> a + b = 8 (2)
Solving the system of equation (1) and (2), we get:
2a = 4 + 8 = 12 --> `a = 6`
`b = a - 4 = 2`
There for:
`(cos (6t) + cos (2t))/2 = cos (2t).cos (4t)`