Question

Seja a função f definida por f(x)= sen x + cos x + cotg x + cossec x - tg x - sec x,
qualquer x diferente de
$\frac{k\pi}{2}$ e $k \in \mathbb{Z}$ (inteiros).
O valor de $f(60^\circ)$

Answer 1

$sinx+cosx+cotx+cscx-tanx-secx$
$sinx+cosx+\frac{cosx}{sinx}+\frac{1}{sinx}-\frac{sinx}{cosx}-\frac{1}{cosx}$
$sin(60)+cos(60)+\frac{cos(60)}{sin(60)}+\frac{1}{sin(60)}-\frac{sin(60)}{cos(60)}-\frac{1}{cos(60)}$
$\frac{\sqrt3}{2}+\frac12+\frac{\frac12}{\frac{\sqrt3}{2}}+\frac{1}{\frac{\sqrt3}{2}}-\frac{\frac{\sqrt3}{2}}{\frac12}-\frac{1}{\frac12}$
$\frac{\sqrt3}{2}+\frac12+\frac{1}{\sqrt3}+\frac{2}{\sqrt3}-\sqrt3-2$
$\frac{3+\sqrt3+2+4-6-4\sqrt3}{2\sqrt3}=\frac{3-3\sqrt3}{2\sqrt3}=\frac{3\sqrt3-9}{6}=\boxed{\frac{\sqrt3-3}{2}}$