壹
如上图:
\[\begin{eqnarray}
已知: \enspace AC=\sin\alpha,BC=\cos\alpha
\\ \\ \\
\sin\left(\frac{\pi}{2}-\alpha\right)=\frac{AD}{AB}=\frac{BC}{AB}=\cos\alpha
\\ \\
诱导公式组0.1: \enspace \sin\left(\frac{\pi}{2}-\alpha\right)=\cos\alpha
\\ \\ \\
\cos\left(\frac{\pi}{2}-\alpha\right)=\frac{BD}{AB}=\frac{AC}{AB}=\sin\alpha
\\ \\
诱导公式组0.2: \enspace \cos\left(\frac{\pi}{2}-\alpha\right)=\sin\alpha
\\ \\ \\
\tan\left(\frac{\pi}{2}-\alpha\right)=\frac{AD}{BD}=\frac{BC}{AC}=\frac{\cos\alpha}{\sin\alpha}
\\ \\
\because \tan\alpha=\frac{\sin\alpha}{\cos\alpha}
\\ \\
诱导公式组0.3: \enspace \tan\left(\frac{\pi}{2}-\alpha\right)=\frac{1}{\tan\alpha}=\cot\alpha
\\ \\ \\诱导公式0.1: \enspace \sin\left(\frac{\pi}{2}-\alpha\right)=\cos\alpha
\\
诱导公式0.2: \enspace \cos\left(\frac{\pi}{2}-\alpha\right)=\sin\alpha
\\
诱导公式0.3: \enspace \tan\left(\frac{\pi}{2}-\alpha\right)=\frac{1}{\tan\alpha}=\cot\alpha
\end{eqnarray}
\]
