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Question

CMR:$\sin 10\sin 50\sin 70=\cos 20\cos 40\cos 80=\frac{1}{8}$

score 0 · Answer 1

Giả sử $P=cos20^0cos40^0cos80^0.$ Khi đó có

$P=\frac{8sin20^{0}cos20^{0}cos40^{0}cos80^{0}}{8sin20^{0}}$

$=\frac{4sin40^{0}cos40^0cos80^0}{8sin20^{0}}$

$=\frac{2sin80^0cos80^0}{8sin20^0}$

$=\frac{sin160^0}{8sin20^0}$

$=\frac{sin20^0}{8sin20^0}$

$=\frac{1}{8}.$

Vì $sin10^0=cos80^0,sin50^0=cos40^0,sin70^0=cos20^0$ nên $sin10^0sin50^0sin70^0=cos20^0cos40^0cos80^0=\frac{1}{8}.$

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