几道高一数学题、

来源：百度知道 编辑：UC知道 时间：2024/05/12 07:59:33
求、sin^4(π/16)+sin^4(3π/16)+sin^4(5π/16)+sin^4(7π/16)的值、

求sin150度（1+√3tan10度)的值

1.
[sin(π/16)]^4+[sin(3π/16)]^4+[sin(5π/16)]^4+[sin(7π/16)]^4

=[sin(π/16)]^4+[sin(3π/16)]^4+[cos(3π/16)]^4+[cos(π/16)]^4

={[sin(π/16)]^2+[cos(π/16)]^2}^2 -2*[sin(π/16)]^2*[cos(π/16)]^2 +{[sin(3π/16)]^2+[cos(3π/16)]^2}^2 -2*[sin(3π/16)]^2*[cos(3π/16)]^2

= 2 -(1/2){[sin(π/8)]^2 +[sin(3π/8)]^2}

= 2 -(1/2){[sin(π/8)]^2 +[cos(π/8)]^2}

= 2-(1/2)

= 3/2

2.sin50°(1+√3tan10°)

=2sin50°(cos60°cos10°+sin60°sin10°)/cos10°

=2sin50°cos50°/cos10°

=sin100°/cos10°

=sin80°/cos10°

=cos10°/cos10°

=1