cos^4 A - sin^4 A +1 = 2 cos^2 A.
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Answer:
cos^4a-sin^4a=2cos^2a-1
LHS, (cos^2a+sin^2a)(cos^2a-sin^2a) identity=a^2-b^2=(a+b)(a-b)
1(cos^2a-(1-cos^2a)) identity=sin^2a+cos^2a=1
(cos^2a-1+cos^2a)=2cos^2a-1=RHS
PROVED
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