Answer
$\cot{(\frac{7\pi}{18})}$
Work Step by Step
RECALL:
The cofunction Identities:
(1) $\sin{\theta} = \cos{(\frac{\pi}{2}-\theta)}$
(2) $\cos{\theta} = \sin{(\frac{\pi}{2}-\theta)}$
(3) $\tan{\theta} = \cot{(\frac{\pi}{2}-\theta)}$
(4) $\cot{\theta} = \tan{(\frac{\pi}{2}-\theta)}$
(5) $\csc{\theta} = \sec{(\frac{\pi}{2}-\theta)}$
(6) $\sec{\theta} = \csc{(\frac{\pi}{2}-\theta)}$
Use identity (3) to obtain:
$\tan{\frac{\pi}{9}}
\\= \cot{(\frac{\pi}{2}-\frac{\pi}{9})}
\\= \cot{(\frac{9\pi}{18}-\frac{2\pi}{18})}
\\=\cot{(\frac{7\pi}{18})}$
