Question

En un triángulo rectángulo ABC
(B = 90°), se sabe que:
secA = 4secC. Calcula:
L = tgA + 3tgC​

Answer 1

DESARROLLO:

$\sec(A) = 4 \sec(C) \\ \frac{b}{c} = 4 \times \frac{b}{a} \\ \frac{a}{c} = 4 \\ \frac{a}{4} = c$

$L = \tan(A) + 3 \tan(C) \\ L = \frac{a}{c} + 3×\frac{c}{a} \\ L = 4 + 3×\frac{ \frac{a}{4} }{a} \\ L = 4 + 3×\frac{1}{4} \\ L = \frac{19}{4}$