prove that
(iii) cos (A + B).cos (A – B) = cos?A – sin2B
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Answer:
Yes!
Step-by-step explanation:
(cosAcosB-sinAsinB).(cosAcosB+sinAsinB)
=> cos²Acos²B + cosAcosBsinAsinB - sinAsinBcosAcosB - sin²Asin²B
=> cos²Acos²B - sin²Asin²B
=> (cos²A)(1-sin²B) - (1-cos²A)(sin²B)
=> cos²A - cos²Asin²B - sin²B + sin²Acos²B
=> cos²A - sin²B
HENCE PROVED!
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