tan10*×tan50*×tan70*等于多少?我把它分成分子分母来算,分子上是sin10×sin50×sin70 算得1/8,可分子算不出户来了?

=80

由tan30°=tan10°tan50°tan70°=3分之根号3

用积化和差算
分母cos10°×cos50°×cos70°=1/2×[cos(10°-50°)-cos(10°+50°)]×cos70°=1/2×(cos40°-1/2)×cos70°=1/4×[cos(40°-70°)-cos(40°+70°)]-1/4×cos70°=√3/8+1/4cos70°-1/4cos70°=√3/8
结果√3/3