ข้อตรีโกณ ก.
$cos\frac{\pi }{5} + cos\frac{3\pi }{5}$
$=2cos\frac{2\pi}{5}cos\frac{\pi}{5} $
$=2sin\frac{\pi}{10}cos\frac{\pi}{5}\cdot \frac{cos\frac{\pi}{10} }{cos\frac{\pi}{10}} $
$=\frac{sin\frac{\pi}{5}cos\frac{\pi}{5} }{cos\frac{\pi}{10} }\cdot \frac{2}{2} $
$=\frac{sin\frac{2\pi}{5} }{2cos\frac{\pi}{10} } $
$=\frac{cos\frac{\pi}{10} }{2cos\frac{\pi}{10} } $
$=\frac{1}{2} $
ดังนั้น
$cos\frac{\pi }{5} + cos\frac{3\pi }{5} +cos\pi = \frac{1}{2} - 1 = -\frac{1}{2}$
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