$\mathop {Lt}\limits_{x \to 1} {\left( {1 - x} \right)^{\tan \pi x}} =$

$P=\lim _{x \rightarrow 1}(1-x)^{\tan \pi x}$

$\begin{array}{l}\Rightarrow \quad \ln p=\lim _{x \rightarrow 1} \tan \pi x(1-x) \\ \Rightarrow \ln p=\lim _{x \rightarrow 1}(1-x) \times \frac{\sin \pi x}{\cos \pi x}\end{array}$

$\begin{array}{c}\Rightarrow \ln p=\frac{0}{-1} \\ \Rightarrow \ln P=0 \\ \Rightarrow p=e^{0} \\ \therefore p=1\end{array}$