Question

find lim (c0s x -1 ) / sin x , do not use Lhopitals rule , as x ->0

Answer 1

\[\lim_{x\rightarrow 0}\frac{\cos{x}-1}{\sin{x}}=\lim_{x\rightarrow 0}\frac{-2\sin^2{\frac{x}{2}}}{2\sin{\frac{x}{2}}\cos{\frac{x}{2}}}=-\lim_{x\rightarrow 0}\tan{\frac{x}{2}}=0\]

Answer 2

thx