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Prove thtat cos^4 A - sin^4 A + 1 = 2cos^2 A?

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please explain to me how you would prove the above equation
asked Apr 12, 2013 in TRIGONOMETRY by homeworkhelp Mentor

1 Answer

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cos4A - sin4A + 1

  (a4 - b4) = (a2 -b2)(a2 + b2)

= [(cos2A - sin2A)( cos2A + sin2A)] + 1

 Recall : cos2A + Sin2A = 1

= (cos2A - sin2A)(1) + 1

(cos2A - sin2A) + 1

Recall : cos2A - (1 - cos2A) + 1

cos2A  - 1 + cos2A + 1

2cos2A.

answered Apr 12, 2013 by diane Scholar

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