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Доказать тождества:

1 . (sinх - siny)²+ (cosx-cosy)²= 4sin²(x-y)/2;

2. (sinα+sinβ)²+(cosα+cosβ)²=4cos²(α-β)/2;

3. cos² (α+β) - cos²(α-β)= - sin2α * sin2β;

4. sin² (x+y) - sin²(x-y)= sin2x * sin2y.
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