10°的正弦*50°的正弦*70°的正弦=?

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10°的正弦*50°的正弦*70°的正弦=?
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10°的正弦*50°的正弦*70°的正弦=?
10°的正弦*50°的正弦*70°的正弦=?

10°的正弦*50°的正弦*70°的正弦=?
10°的正弦*50°的正弦*70°的正弦=?
sin10°sin50°sin70°
= 2sin10°cos10°sin50°cos20°/2cos10°
= 2sin20°cos20°sin50°/4cos10°
= 2sin40°cos40°/8cos10°
= sin80°/16cos10°
= cos10°/16cos10°
=1/16

=cos20*cos40*cos80
=(sin20*cos20)/sin20*cos40cos80
=1/2sin40cos40cos80/sin20
=1/4sin80cos80/sin20
=1/8sin160=1/8*sin20/sin20=1/8

把10'换成80'.50'换成40'70度换成20'然后用倍角公式的逆用公式,去解