If $f(x)=\log \left(\sec ^{2} x\right)^{\cot 2} x$ for $x \neq 0$ $=K$ for $x=$ is continuous at $x=0$ then $K 1 \mathrm{~S}$ $(\mathrm{A}) e^{-1}$ (B) 1 (C) $e$ (D) 0