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Write the expression as a product of trigonometric functions. cos6x−cos2x

User Awenkhh
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Final answer:

The expression cos6x - cos2x can be written as the product of trigonometric functions using the cosine sum-to-product identity, resulting in -2 cos(4x) cos(2x).

Step-by-step explanation:

To express cos6x - cos2x as a product of trigonometric functions, we can use the cosine sum-to-product identity which comes from the sum and difference formulas for cosine. The formula is as follows:

cosα + cosβ = 2 cos((α + β)/2) cos((α - β)/2)

Applying it to our expression with α = 6x and β = 2x, we get:

cos6x - cos2x = -(- cos6x + cos2x)

Now using the sum-to-product formula:

cos6x - cos2x = -2 cos((6x + 2x)/2) cos((6x - 2x)/2)

cos6x - cos2x = -2 cos(4x) cos(2x)

Thus, the given expression can be written as -2 cos(4x) cos(2x).

User Mads Gadeberg
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