两个关于三角函数计算的高中数学题1.sin20°·sin40°·sin60°·sin802.sin6°·cos24°·sin78°·cos48这两题解法思路一样么?
问题描述:
两个关于三角函数计算的高中数学题
1.sin20°·sin40°·sin60°·sin80
2.sin6°·cos24°·sin78°·cos48
这两题解法思路一样么?
答
sin(6°)cos(12°)cos(24°)cos(48°)
=sin6°·cos6°·cos12°·cos24°·cos48°/cos6°
=sin12°·cos12°·cos24°·cos48°/2cos6°
=sin24°·cos24°·cos48°/4cos6°
=sin48°·cos48°/8cos6°
=sin96°/16cos6°
=sin(180°-96°)/16cos6°
=sin84°/16cos6°
=1/16