Question

高中数学 sin10°sin50°sin70° 怎样化简求值？？

Answer 1

sin10°sin50°sin70°=1/2(2cos10°sin10°sin50°sin70°）/cos10°
=1/2(sin20°cos20°sin50°）/cos10°=1/4(sin40°cos40°）/cos10°
=1/8sin80°/cos10°=1/8cos10°/cos10°=1/8

Answer 2

分子和分母同时乘以 cos10°

sin10°×sin50°×sin70°
= sin10°×sin50°×sin70°× cos10°/cos10°
= (1/2) × sin20°× sin50°× sin70°/cos10°
= (1/2) × sin20°× sin50°× cos20°/cos10°
= (1/4) × sin40°× sin50°/cos10°
= (1/4) × sin40°× cos40°/cos10°
= (1/8) × sin80°/cos10°
= (1/8) × sin80°/sin80°
= 1/8

Answer 3

运用公式sin2A=2sinAcosA
sin10°sin50°sin70°
=(sin10°cos10°sin50°sin70°)/(cos10°)
=(sin20°sin50°sin70°)/(2cos10°)
=(sin20°sin50°cos20°)/(2cos10°)
=(sin40°sin50°)/(4cos10°)
=(sin40°cos40°)/(4cos10°)
=sin80°/(8cos10°)
=1/8