2. If the real number $\alpha$ satisfies $\cos \alpha=\tan \alpha$, then the value of $\frac{1}{\sin \alpha}+\cos ^{4} \alpha$ is
Answer: 2. Solution: From the condition, we know that $\cos ^{2} \alpha=\sin \alpha$. Repeatedly using this conclusion and noting that $\cos ^{2} \alpha+\sin ^{2} \alpha=1$,
$$
\begin{array}{l}
\text { we get } \frac{1}{\sin \alpha}+\cos ^{4} \alpha=\frac{\cos ^{2} \alpha+\sin ^{2} \alpha}{\sin \alpha}+\sin ^{2} \alpha=(1+\sin \alpha)\left(1-\cos ^{2} \alpha\right) \\
=2+\sin \alpha-\cos ^{2} \alpha=2 .
\end{array}
$$