resolver limite de função trigonométrica composta

[Romeiro bastos]

\(\lim_{x\to 0}cos \left ( \frac{\sin x-\pi }{2x} \right )\)

[Man Utd]

é isto \(\lim_{x \rightarrow 0} cos(\frac{sen(x-\pi)}{2x})\)mesmo???

se for, então segue a resolução :

\(\\\\\\ cos(\lim_{x \rightarrow 0} \frac{sen(x-\pi)}{2x}) \\\\\\ cos(\frac{1}{2}*\lim_{x \rightarrow 0} \frac{sen(x-\pi)}{x}) \\\\\\ cos(\frac{1}{2}*\lim_{x \rightarrow 0} \frac{senx*cos\pi-sen\pi*cosx}{x}) \\\\\\ cos(\frac{1}{2}*\lim_{x \rightarrow 0} -\frac{senx}{x}) \\\\\\ cos(\frac{1}{2}*(-1))\\\\\\ cos(-\frac{1}{2}) \\\\ cos(\frac{1}{2})\)