Prove that 2 cos² A- cos⁴ A + sin⁴ A= 2
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Step-by-step explanation:
2 cos² A- cos⁴ A + sin⁴ A
2 cos² A+ sin⁴ A - cos⁴ A
2 cos² A + (sin^2 A)^2 - (cos^2 A) ^2
2 cos² A + ( sin^2A + cos^2A) (sin^2A - cos^2A)
2 cos² A + 1×(sin^2A - cos^2A)
2 cos² A + sin^2A - cos^2A
sin^2A + cos^2A
1
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