问一道高中三角函数数学题

题目

问一道高中三角函数数学题
求sin10°sin50°sin70°的值

答案

分子 分母 同时乘以 cos10°
sin10°×sin50°×sin70°
= sin10°×sin50°×sin70°× cos10°/cos10°
= sin10°× cos10°×sin50°×sin70°/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