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Prove that 1-cos5Acos3A-sin5Asin3A=2sin^2A Please give every steps if possible for...
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We'll re-write the expression:
1 - (cos 5Acos3A + sin5Asin3A) = 2`sin^2 A`
We'll use the identity:
cos(a-b) = cos a*cos b + sin a*sin b
(cos 5Acos3A + sin5Asin3A) = cos (5A-3A)
(cos 5Acos3A + sin5Asin3A) = cos 2A
1 - cos 2A = `2sin^2A`
cos 2A = 1 - `2sin^2 A`
Since we've get the double angle identity, that means that the given expression represents an identity.
Posted by giorgiana1976 on August 29, 2011 at 12:45 AM (Answer #1)
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