两个关于三角函数计算的高中数学题
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/07/31 00:51:47
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?
1.sin20°·sin40°·sin60°·sin80
2.sin6°·cos24°·sin78°·cos48
这两题解法思路一样么?
![两个关于三角函数计算的高中数学题](/uploads/image/z/6313314-66-4.jpg?t=%E4%B8%A4%E4%B8%AA%E5%85%B3%E4%BA%8E%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E8%AE%A1%E7%AE%97%E7%9A%84%E9%AB%98%E4%B8%AD%E6%95%B0%E5%AD%A6%E9%A2%98)
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
=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