Question

Sabendo que sen (x) - cos (x) = 0,4, sen (2x) é igual a :
a- 0,84
b- 0,6
c- 0,36
d- 0,64
e- 0,8

PRECISA DE RESOLUÇÃO

Answer 1

$\text{sen(x)}-\text{cos(x)}=0,4 \\\\ \ [ \ \text{sen(x)}-\text{cos(x)} \ ] ^2 = (0,4)^2 \\\\ \text{sen}^2(\text x)-2.\text{sen(x).cos(x)}+\text{cos}^2(\text x) = 0,16 \\\\ \underline{\text{sabemos que}}: \\\\ \text{sen}^2(\text x)+\text{cos}^2(\text x)=1 \\\\\ \text{sen(2x)}=2\text{sen(x).cos(x)} \\\\ \underline{\text{Da{\'i}}}: \\\\ \text{sen}^2(\text x)-2.\text{sen(x).cos(x)}+\text{cos}^2(\text x) = 0,16 \\\\ 1-\text{sen(2x)}=0,16 \\\\ \text{sen(2x) } = 1-0,16 \\\\ \huge\boxed{\text{sen(2x)} = 0,84\ }$

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