Question

contestar y simplificar ​

Answer 1

Respuesta:

sec(x)

Explicación paso a paso:

$tan(x) = \frac{sen(x)}{cos(x)}\\\\\frac{sen(x)}{cos(x)} + \frac{cos(x)}{1+sen(x)} \\\\\frac{sen(x)(1+sen(x)) + cos(x)cos(x)}{cos(x)(1+sen(x))}\\\\\frac{sen(x) + sen^{2}(x) + cos^{2}(x)}{cos(x)(1+sen(x))}$

Por identidad pitagórica:

$sen^{2}(x) + cos^{2} (x) = 1\\\\\frac{sen(x) + 1}{cos(x)(1+ sen(x))}\\\\\frac{1}{cos(x)} = sec(x)$