[กิตติ]

13.จงหาค่าของ $cos\frac{\pi }{7} -cos\frac{2\pi }{7} +cos\frac{3\pi }{7}$

ตอบ$\frac{1}{2} $
$cos\frac{\pi }{7} -cos\frac{2\pi }{7} +cos\frac{3\pi }{7}$
$=\dfrac{2cos\frac{\pi }{14} }{2cos\frac{\pi }{14} }\left[\,\right.cos\frac{\pi }{7} -cos\frac{2\pi }{7} +cos\frac{3\pi }{7}\left.\,\right] $
$=\dfrac{1}{2cos\frac{\pi }{14}} \left[\,\right.2cos\frac{\pi }{14} cos\frac{\pi }{7} -2cos\frac{\pi }{14}cos\frac{2\pi }{7} +2cos\frac{\pi }{14}cos\frac{3\pi }{7}\left.\,\right] $
$=\dfrac{1}{2cos\frac{\pi }{14}} \left[\,\right.(cos\frac{3\pi }{14}+cos\frac{\pi }{14})-(cos\frac{5\pi }{14}+cos\frac{3\pi }{14})+(cos\frac{7\pi }{14}+cos\frac{5\pi }{14})\left.\,\right] $
$=\dfrac{1}{2cos\frac{\pi }{14}} \left[\,\right.(cos\frac{\pi }{14}+cos\frac{\pi }{2})\left.
\,\right] $
$cos\frac{\pi }{2}=0$

$cos\frac{\pi }{7} -cos\frac{2\pi }{7} +cos\frac{3\pi }{7} = \frac{1}{2}$