If sinA+ sinB=a and cosA+cosB = b,then cos(A+B) is
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Cos2A+Cos2B+2Cos(A+B) = b2-a2. So, 2Cos(A+B)Cos(A-B)+2Cos(A+B) = b2-a2. You'd get Cos(A+B){a2+b2) = (b2-a2).
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