Matematika

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Nilai eksak dari cos² 36° cos² 72 adalah ...

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  • Bab Trigonometri
    Matematika SMA Kelas X

    cos² 36° . cos² 72
    = cos 36° . cos 72° . cos 36° . cos 72° . (2 . 2)/(2 . 2)
    = (2 . cos 36°. cos 72°) . (2 . cos 36° . cos 72°)/4
    = (1/4) . ((2 . sin 36° cos 36°. cos 72°)/(sin 36°)) . ((2 . sin 36°. cos 36°. cos 72°)/(sin 36°))
    = (1/4) . ((sin (2 . 36°) . cos 72°)/(sin 36°)) . ((sin (2 . 36°) . cos 72°)/sin 36°)
    = (1/4) . ((sin 72°. cos 72°)/(sin 36°)) . ((sin 72° . cos 72°)/(sin 36°))
    = (1/4) . ((2 . sin 72°. cos 72°)/(2 . sin 36°)) . ((2 . sin 72°. cos 72°)/(2 . sin 36°)
    = (1/16) . ((sin (2 . 72°))/(sin 36°)) . ((sin (2 . 72°)/(sin 36°))
    = (1/16) . ((sin 144°)/(sin 36°)) . ((sin 144°)/(sin 36°))
    = (1/16) . ((sin (180° - 36°))/(sin 36°)) . (sin (180° - 36°))/(sin 36°))
    = (1/16) . ((sin 36°) / (sin 36°)) . ((sin 36°) / (sin 36°))
    = (1/16) . 1 . 1
    = 1/16

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