Prove that cos (A+B) cos (A-B) = cos²A-sin²B
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Answer:
LHS:
= cos (A + B) cos (A - B)
= (cosA cosB - sinA sinB) (cosA cosB + sinA sinB)
= cos²A cos²B - sin²A sin²B
= cos²A (1 - sin²B) - sin²B (1 - cos²A)
= cos²A - cos²A sin²B - sin²B+ cos²A sin²B
= cos²A -sin²B
LHS = RHS
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