Question

sin20°?sin40°?sin60°?sin80°的值为（　　）A．116B．?116C．316D．-31

sin20°?sin40°?sin60°?sin80°的值为（　　）A．116B．?116C．316D．-316

Answer 1

sin20°?sin40°?sin60°?sin80°
=

1

2

[cos（20°-40°）-cos（20°+40°）]sin80°sin60°
=

1

2

（cos20°sin80°-cos60°sin80°）sin60°
=

1

2

{

1

2

[sin（20°+80°）+sin（80°-20°）]-

1

2

sin80°}sin60°
=

1

2

{

1

2

[sin100°+sin60°]-

1

2

sin80°}sin60°
=

1

2

{

1

2

sin80°+

1

2

sin60°-

1

2

sin80°}sin60°
=

1

4

sin²60°
=

3

16

．
故选C