Cos²α+cos²β-cos(α+β)cos(α-β)

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вопрос

The given expression is in the form of the trigonometric identity:

cos²α + cos²β - cos(α+β)cos(α-β) = cos²α + cos²β - [cos²α - sinαsinβ][cos²α + sinαsinβ]

Expanding the expression:
= cos²α + cos²β - cos²αcos²α - cos²αsinαsinβ + cos²βsinαsinβ - sinαsinβsinαsinβ
= cos²α + cos²β - cos²α + cos²αsinαsinβ + cos²βsinαsinβ - sin²αsin²β
= cos²β + sin²β
= 1

Therefore, the given expression simplifies to 1.