Question

comprueba la siguiente identidad trigonometrica
[csc(A)-cot(A)][sec(A)+1]=tan(A)
xfis ayuden

Answer 1

Explicación paso a paso:

$[csc(A) - cot(A)][sec(A) + 1] = tan(A)$

$[ \frac{1}{sen(A)} - \frac{cos(A)}{sen(A)} ][ \frac{1}{cos(A)} + \frac{cos(A)}{cos(A)} ] = tan(A)$

$[ \frac{1 - cos(A)}{sen(A)} ] [ \frac{1 + cos(A)}{cos(A)} ] = tan(A)$

$\frac{ {1}^{2} - {cos}^{2}(A)}{[sen(A)][cos(A)]} = tan(A)$

$\frac{ {sen}^{2}(A)}{[sen(A)][cos(A)]} = tan(A)$

$\frac{sen(A)}{cos(A)} = tan(A)$

$tan(A) = tan(A)$