## Trigonometry (11th Edition) Clone

We fill in the blank with $\tan$.
$$\cot\frac{\pi}{3}=A\frac{\pi}{6}\hspace{1cm}(1)$$ We notice that $$\frac{\pi}{3}+\frac{\pi}{6}=\frac{2\pi+\pi}{6}=\frac{3\pi}{6}=\frac{\pi}{2}$$ That means we can rewrite $(1)$ as $$\cot\frac{\pi}{3}=A(\frac{\pi}{2}-\frac{\pi}{3})$$ Now from the Cofunction Identity: $$\cot\theta=\tan(\frac{\pi}{2}-\theta)$$ So $$A=\tan$$ In other words, we fill in the blank with $\tan$.