Question

prove that cos2Acos2B+sin²(A-B)-sin²(A+B)= 2cos(A+B). Please don't spam it's urgent​

Answer 1

Answer:

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

+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)