Question

How do you use the sum to product formulas to write the sum or difference `cos120^circ+cos30^circ` as a product?

Answer 1

`2cos (75^@).cos (45^@)`

Explanation:

Use trig identity:
`cos a + cos b = 2cos ((a + b)/2)cos ((a - b)/2)`
In this case:
`cos ((a + b)/2) = cos (75)`, and cos `((a - b)/2) = cos (45)`
There for:
`cos 120 + cos 30 = 2 cos (75).cos (45)`