高一数学三角恒等变题..1 cos36°cos72°=?2 sin10°sin30°sin50°sin70°=?

高一数学三角恒等变题..1 cos36°cos72°=?2 sin10°sin30°sin50°sin70°=?
高一数学三角恒等变题..
1 cos36°cos72°=?
2 sin10°sin30°sin50°sin70°=?

高一数学三角恒等变题..1 cos36°cos72°=?2 sin10°sin30°sin50°sin70°=?
1 cos36°cos72°
= 2sin36cos36°cos72°/2sin36
=sin72cos72/2sin36
=sin144/4sin36
=sin36/4sin36
=1/4
2 sin10°sin30°sin50°sin70°
=cos80cos60cos40cos20
=1/2cos20cos40cos80
=2sin20cos20cos40cos80/4sin20
=sin40cos40cos80/4sin20
=sin80cos80/8sin20
=sin160/16sin20
=sin20/16sin20
=1/16

1)cos36°cos72°=2sin36°cos36°cos72°/(2sin36°)
=sin72°cos72°/(2sin36°)
=sin144°/(4sin36°)
=sin36°/(4sin36°)
...

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1)cos36°cos72°=2sin36°cos36°cos72°/(2sin36°)
=sin72°cos72°/(2sin36°)
=sin144°/(4sin36°)
=sin36°/(4sin36°)
=1/4
2)与上式一样原理：
sin10°sin30°sin50°sin70°=2cos10°sin10°sin30°sin50°sin70°/(2cos10°)
=sin20°sin30°sin50°sin70°/(2cos10)
=sin20°*1/2*cos40°*cos20°/(2cos10°)
=sin40°cos40°/(8cos10°)
=sin80°/(16cos10°)
=1/16

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1cos72°cos36°
=2sin36°cos72°cos36°/2sin36°
=sin72°cos72°/2sin36° =2sin72°cos72°/4sin36°
=sin144°/4sin36° =sin36°/4sin36° =1/4
.2.sin10*sin30*sin50*sin70
=cos10*sin10*sin30*sin5...

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1cos72°cos36°
=2sin36°cos72°cos36°/2sin36°
=sin72°cos72°/2sin36° =2sin72°cos72°/4sin36°
=sin144°/4sin36° =sin36°/4sin36° =1/4
.2.sin10*sin30*sin50*sin70
=cos10*sin10*sin30*sin50*sin70/cos10
=1/2*sin20*sin70*sin30*sin50/cos10
=1/2*sin20*cos20*sin30*sin50/cos10
=1/4sin40*sin50*sin30/cos10
=1/4sin40*cos40*sin30/cos10
=1/8sin80*sin30/cos10
=1/8cos10*sin30/cos10
=1/8sin30
=1/16

收起

1、cos36°cos72°=2sin36°cos36°cos72°/(2sin36°)
=sin72°cos72°/(2sin36°)
=sin144°/(4sin36°)
=sin36°/(4sin36°)
...

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1、cos36°cos72°=2sin36°cos36°cos72°/(2sin36°)
=sin72°cos72°/(2sin36°)
=sin144°/(4sin36°)
=sin36°/(4sin36°)
=1/4
2、sin10°sin30°sin50°sin70°=cos80°cos60°cos40°cos20°
=cos80°cos60°cos40°cos20°sin20°/sin20°
=cos80°cos60°cos40°sin40°/2sin20°
=cos80°cos60°sin80°/4sin20°
=sin160°cos60°/8sin20°
=1/16

收起