Question

Sabendo que x = π/6, qual valor de y?

Answer 1

$\displaystyle \text{y}=\frac{\text{cossec(x) + sen(x)}}{\text{cotg}^2(\text x)} \\\\\\ \text{y} = \frac{\displaystyle \frac{1}{\text{sen(x)}}+\text{sen(x)}}{\displaystyle \frac{1}{\text{tg}^2(\text x)}} \\\\\\\\ \text y= \frac{\displaystyle \frac{1+\text{sen}^2(\text x)}{\text{sen(x)}}}{\displaystyle \frac{1}{\text{tg}^2(\text x)}} \\\\\\\ \text y = \frac{[1+\text{sen}^2(\text x)]}{\text{sen(x)}}.\text{tg}^2(\text x) \\\\\\ \text{x}=\frac{\pi}{6} = 30^\circ \\\\ \underline{\text{substituindo}}:$

$\displaystyle \text y = \frac{[1+\text{sen}^2(30^\circ)]}{\text{sen}(30^\circ)}.\text{tg}^2(30^\circ) \\\\\\ \text y = \frac{[\displaystyle 1+(\frac{1}{2})^2]}{\displaystyle \frac{1}{2}}.(\frac{\sqrt3}{3})^2 \\\\\\\ \text y = \frac{\displaystyle [1+\frac{1}{4}]}{\displaystyle \frac{1}{2}}.\frac{3}{9} \\\\\\\ \text y = \frac{5}{4}.\frac{2}{1}.\frac{1}{3} \\\\\ \\ \ \huge\boxed{\text y = \frac{5}{6}\ }\checkmark$