x=asin^2A+bcos^2A prove that (x-a) (b-x) = (a-b) ^2 sin^2Acos^2A
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Step-by-step explanation:
x=asin²A+bcos²A
(x-a) (b-x) = [asin²A + bcos²A - a][b - asin²A - bcos²A]
= [bcos²A - a(1-sin²A)][b(1-cos²A) - asin²A]
= [bcos²A - acos²A][bsin²A - asin²A]
= [(b-a)cos²A][(b-a)sin²A]
= [-(a-b)cos²A] [-(a-b)sin²A]
= (a-b)cos²Asin²A
= R.H.S.
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