Answer 1

\[\lim_{x \to 0^-} \left[ 1 + \cos ec  x \right]\]
\[Let x = 0 - \text{ h, where h } \to 0 . \]
\[ \lim_{h \to 0} \left[ 1 + cosec \left( - h \right) \right]\]
\[ = \lim_{h \to 0} \left[ 1 - cosec h \right] \left[ cosec \left( - \theta \right) = - cosec \theta \right]\]
\[ = 1 - \infty \]
\[ = - \infty\]