Question

Mostre que cos^4 x + sen^4 x + 2 (sen(x) . cos(x))² = 1

Answer 1

Resposta:

Explicação passo-a-passo:

cos^4 x + sen^4 x = (cos²x+sen²x)² - 2sen²x.cos²x

cos^4 x + sen^4 x = (1)² - 2sen²x.cos²x

cos^4 x + sen^4 x = 1 - 2(senx.cosx)²

2(senx.cosx)² = 1 - (cos^4 x + sen^4 x)

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cos^4 x + sen^4 x + 1 - (cos^4 x + sen^4 x)

cos^4 x + sen^4 x + 1 - cos^4 x - sen^4 x =

1