Question

The value of the expression $4(\sin \frac{7\pi }{6}\cos \frac{2\pi }{3}+\tan \frac{\pi }{8}\cos \frac{\pi }{8}+\sin \frac{9\pi }{8})$ is

Answer 1

$4(\sin \frac{7\pi }{6}\cos \frac{2\pi }{3}+\tan \frac{\pi }{8}\cos \frac{\pi }{8}+\sin \frac{9\pi }{8})=(\sin (\pi +\frac{\pi }{6})\cos (\frac{\pi }{2}+\frac{\pi }{6})+\tan \frac{\pi }{8}\cos \frac{\pi }{8}+\sin (\pi +\frac{\pi }{8}))=(-\sin \frac{\pi }{6}(-\sin \frac{\pi }{6})+\sin \frac{\pi }{8}-\sin \frac{\pi }{8})=4{\sin }^2\frac{\pi }{6}=1$