2 sin2 A + cos4 A – 1 is equal to ______.

Question

KollegeApply · Accepted Answer

2 sin2 A + cos4 A – 1 is equal to sin4 A. Explanation: sin2 A + cos2 A = 1 cos2 A = 1 − sin2 A 2 sin2 A + (1 − sin2 A)2 − 1 Use the algebraic identity (a − b)2 = a2 − 2ab + b2 where a = 1 and b = sin2 A: (1 − sin2 A)2 = 1 − 2 sin2 A + (sin2 A)2 (1 − sin2 A)2 = 1 − 2 sin2 A + sin4 A 2 sin2 A + (1 − 2 sin2 A + sin4 A) − 1 (2 sin2 A − 2 sin2 A) + (1 − 1) + sin4 A 0 + 0 + sin4 A = sin4 A

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