Converst trigonometrical sum in product

Question

I'm starting to work with some trigonometrical properties and I got the following problem:

Convert the following sum into a product: $\cos{x} + \cos{3x} + \cos{5x} + \cos{7x}$

Using the property with states: $\cos{\alpha} + \cos{\beta} = 2 \times \cos{\frac{\alpha + \beta}{2}} \times \cos{\frac{\alpha - \beta}{2}}$.

I got:

$2 \times \cos^2{2x} + 2 \times \cos{6x} \times \cos{x}$

How to proceed now ?

http://math.stackexchange.com/questions/117114/sum-cos-when-angles-are-in-arithmetic-progression — lab bhattacharjee, Feb 23 '14 at 19:26

score 1 · Accepted Answer · answered Feb 23 '14 at 19:30

1

$$\cos x+\cos7x=2\cos3x\cos4x$$ and $$\cos3x+\cos5x=2\cos x\cos4x$$

Taking out $2\cos4x,$ $$\cos x+\cos3x=?$$

answered Feb 23 '14 at 19:30

lab bhattacharjee

1 Answers1