Question

AYUDENNNMEEEE



En un triangulo rectangulo ABC

(B=90°)

K= sen C / sec C + sen C / sec A

Answer 1

DESARROLLO:

Tenemos los siguientes datos:

${a}^{2} + {c}^{2} = {b}^{2}$

$sen(c) = \frac{c}{b}$

$sec(c) = \frac{b}{a}$

$sen(a) = \frac{a}{b}$

$sec(a) = \frac{b}{c}$

Entonces:

$k = \frac{sen(a)}{sec(c)} + \frac{sen(c)}{sec(a)}$

$k = \frac{ \frac{a}{b} }{ \frac{b}{a} } + \frac{ \frac{c}{b} }{ \frac{b}{c} }$

$k = \frac{ {a}^{2} }{ {b}^{2} } + \frac{ {c}^{2} }{ {b}^{2} }$

$k = \frac{ {a}^{2} + {c}^{2} }{ {b}^{2} }$

$k = \frac{ {b}^{2} }{ {b}^{2} } = 1$

Un gusto espero que te sirva.