Answer
$\sin{(\frac{\pi}{10})}$
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 (2) to obtain:
$\cos{\frac{2\pi}{5}}
\\= \sin{(\frac{\pi}{2}-\frac{2\pi}{5})}
\\= \sin{(\frac{5\pi}{10}-\frac{4\pi}{10})}
\\=\sin{(\frac{\pi}{10})}$
