Quiz , 50 poinbuktikan bahwa cos π/7 – cos 2π/7 + cos 3π/7 = ½ no ngasalno spampakai cara November 30, 2021 by Skylar Quiz , 50 poin buktikan bahwa cos π/7 – cos 2π/7 + cos 3π/7 = ½ no ngasalno spampakai cara
[tex]\cos( \frac{\pi}{7} ) + \cos( \frac{2\pi}{7} ) + \cos( \frac{3\pi}{7} ) \\ = (\cos( \frac{\pi}{7} ) + \cos( \frac{2\pi}{7} ) + \cos( \frac{3\pi}{7} ) ) \: ( \frac{2 \sin( \frac{2\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } ) \\ = \frac{2 \sin( \frac{2\pi}{7} ) \cos( \frac{\pi}{7} ) – 2 \sin( \frac{2\pi}{7} ) \cos( \frac{2\pi}{7} ) + 2 \sin( \frac{2\pi}{7} ) \cos( \frac{3\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{( \sin( \frac{3\pi}{7} ) + \sin( \frac{\pi}{7} ) ) – \sin( \frac{4\pi}{7} ) ( \sin( \frac{5\pi}{7} ) – \sin( \frac{\pi}{7} ) ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{ \: \sin( \frac{3\pi}{7} ) – \sin( \frac{4\pi}{7} ) + \sin( \frac{5\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{\sin( \frac{7\pi – 4\pi}{7} ) – \sin( \frac{4\pi}{7} ) + \sin( \frac{7\pi – 2\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{ \sin( \frac{4\pi}{7} ) – \sin( \frac{4\pi}{7} ) + \sin( \frac{2\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{ \sin( \frac{2\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{1}{2} \\ jadi \: terbukti \: \cos( \frac{\pi}{7} ) – \cos( \frac{2\pi}{7} ) + \cos( \frac{3\pi}{7} ) = \frac{1}{2} [/tex] Reply
[tex]\cos( \frac{\pi}{7} ) + \cos( \frac{2\pi}{7} ) + \cos( \frac{3\pi}{7} ) \\ = (\cos( \frac{\pi}{7} ) + \cos( \frac{2\pi}{7} ) + \cos( \frac{3\pi}{7} ) ) \: ( \frac{2 \sin( \frac{2\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } ) \\ = \frac{2 \sin( \frac{2\pi}{7} ) \cos( \frac{\pi}{7} ) – 2 \sin( \frac{2\pi}{7} ) \cos( \frac{2\pi}{7} ) + 2 \sin( \frac{2\pi}{7} ) \cos( \frac{3\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{( \sin( \frac{3\pi}{7} ) + \sin( \frac{\pi}{7} ) ) – \sin( \frac{4\pi}{7} ) ( \sin( \frac{5\pi}{7} ) – \sin( \frac{\pi}{7} ) ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{ \: \sin( \frac{3\pi}{7} ) – \sin( \frac{4\pi}{7} ) + \sin( \frac{5\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{\sin( \frac{7\pi – 4\pi}{7} ) – \sin( \frac{4\pi}{7} ) + \sin( \frac{7\pi – 2\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{ \sin( \frac{4\pi}{7} ) – \sin( \frac{4\pi}{7} ) + \sin( \frac{2\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{ \sin( \frac{2\pi}{7} ) }{2 \sin( \frac{2\pi}{7} ) } \\ = \frac{1}{2} \\ jadi \: terbukti \: \cos( \frac{\pi}{7} ) – \cos( \frac{2\pi}{7} ) + \cos( \frac{3\pi}{7} ) = \frac{1}{2} [/tex]