Question

Se cos.x + sen.x = raiz de 2, então sen (2x)= ? Me ajudem por favor.

Answer 1

cosx + senx = √2

(cosx + senx)² = (√2)²

(cos²x+sen²x) +[2.cosx.senx] = 2

(1) +[sen 2x] = 2

sen 2x = 1 ✓

Answer 2

$Sen(2x) = 2\cdot sen\ x\cdot cos\ x\\\\cos\ x + sen\ x = \sqrt{2} \\(cos\ x + sen\ x)^2 = (\sqrt{2})^2\\cos^2\ x + 2\cdot sen\ x\cdot cos\ x + sen^2 x = 2\\\\cos^2\ x + sen^2\ x + 2\cdot sen\ x\cdot cos\ x = 2\\\\\mathsf{Ja\ que\ "cos^2\ x + sen^2\ x = 1"}\\\\1 + 2\cdot sen\ x\cdot cos\ x = 2\\2\cdot sen\ x\cdot cos\ x = 1\\\\\mathsf{2\cdot sen\ x\cdot cos\ x\ = sen(2x)}\\\\\mathsf{Logo,}\\\\\boxed{\mathsf{sen(2x) = 1}}$

Abraços!