Задача тригонометрия

[Гост]

Добро утро! Може ли помощ? Благодаря, хубав ден!

[S.B.]

[tex]A = \frac{2sin\alpha + cos\alpha}{5sin\alpha - 3cos\alpha}= \frac{sin\alpha(2 + cotg\alpha)}{sin\alpha(5 - 3cotg\alpha)} = \frac{2 + cotg\alpha}{5 - 3cotg\alpha}[/tex]

$cotg\alpha = \frac{3}{4}$

[tex]A = \displaystyle\frac{2 + cotg\alpha}{5 - 3cotg\alpha } = \displaystyle\frac{2 + \displaystyle\frac{3}{4}}{5 - \displaystyle\frac{9}{4}} = \displaystyle\frac{\displaystyle\frac{11}{4}}{\displaystyle\frac{11}{4}} = 1[/tex]