Question

cos2Acos2B + sin²(A-B) - sin²(A+B) = cos(2A+2B)

Answer 1

+sin²(A-B) = (sinAcosB - cosAsinB)²
-sin²(A+B) = (sinAcosB - cosAsinB)²
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-4sinAcosBcosAsinB
= -(2sinAcosA)(2sinBcosB)
= -sin2Asin2B

so,

cos2Acos2B - sin2Asin2B = cos(2A+2B)