) cos 5x.cos x - cos 4x•cos 2x

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To simplify the expression cos(5x)cos(x) - cos(4x)cos(2x), we can use the trigonometric identity cos(a)cos(b) = 0.5[cos(a+b) + cos(a-b)].

Applying this identity to the given expression, we have:

= 0.5[cos(5x+x) + cos(5x-x)] - 0.5[cos(4x+2x) + cos(4x-2x)]
= 0.5[cos(6x) + cos(4x)] - 0.5[cos(6x) + cos(2x)]
= 0.5cos(6x) + 0.5cos(4x) - 0.5cos(6x) - 0.5cos(2x)
= 0.5cos(4x) - 0.5cos(2x)

Therefore, cos(5x)cos(x) - cos(4x)cos(2x) simplifies to 0.5cos(4x) - 0.5cos(2x).