Question

2cos2b.cos(A-B)= cos(A+B)+cos(A-3b)

Answer 1

Cos(A+B)cos(A−B)≡(cosAcosB−sinAsinB)(cosAcosB+sinAsinB)≡cos2Acos2B−sin2Asin2B≡cos2A(1−sin2B)−(1−cos2A)sin2B≡cos2A−cos2Asin2B−sin2B+cos2Asin2B≡cos2A−sin2B

Answer 2

Answer:

Cos(A+B)cos(A−B)≡(cosAcosB−sinAsinB)(cosAcosB+sinAsinB)≡cos2Acos2B−sin2Asin2B≡cos2A(1−sin2B)−(1−cos2A)sin2B≡cos2A−cos2Asin2B−sin2B+cos2Asin2B≡cos2A−sin2B