(cosA- cos B) (sin A- Sin B) =
4 sin (A-B/2)
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Step-by-step explanation:
=> (cos^2A + cos^2B + 2cosAcosB) + (sin^2A + sin^2B - 2sinAsinB)
=> cos^2A + cos^2B + sin^2A + sin^2B + 2cosAcosB - 2sinAsinB
=> cos^2A + sin^2A + cos^2B + sin^2B + 2(cosA*cosB - sinA*sinB)
=> 1 + 1 + 2(cosA*cosB - sinA*sinB)
=> 2 + 2(cosA*cosB - sinA*sinB)
=> 2 (1 + (cosA*cosB + sinA*sinB))
=> 2 * (1 + cos(A-B))
{Because: cosA*cosB - sinA*sinB = cos(A+B)}
=> 2 * 2cos^2 ((A+B)/2)
=> 4cos^2 (A+B)/2
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