Question

Cos 6альфа - cos 3альфа=

Answer 1

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Answer 2

The expression you've given, "cos(6α) - cos(3α)," is a trigonometric expression involving the cosine function. To simplify this expression, you can use trigonometric identities.

One identity that can be useful here is the sum-to-product identity for cosine:

$\cos(A) - \cos(B) = -2 \sin\left(\frac{A + B}{2}\right) \sin\left(\frac{A - B}{2}\right)$

In your case, if you set $A = 6α$ and $B = 3α$, you get:

$\cos(6α) - \cos(3α) = -2 \sin\left(\frac{6α + 3α}{2}\right) \sin\left(\frac{6α - 3α}{2}\right)$

Simplifying the angles inside the sine functions:

$\cos(6α) - \cos(3α) = -2 \sin\left(\frac{9α}{2}\right) \sin\left(\frac{3α}{2}\right)$

So, the simplified expression for $\cos(6α) - \cos(3α)$ is $-2 \sin\left(\frac{9α}{2}\right) \sin\left(\frac{3α}{2}\right)$.