sin15°sin105°
=sin15°sin(90°+15°)←使用诱导公式
=sin15°cos15°
=0.5×(2sin15°cos15°)←使用二倍角公式
=0.5×sin30°
=0.5×0.5
=0.25
=1/4
sin15°sin105°
=sin(45°-30°)sin(45°+60°)
=(sin45°cos30°-cos45°sin30°)(sin45°cos60°+cos45°sin60°)
=(√2/2×√3/2-√2/2×0.5)(√2/2×0.5+√2/2×√3/2)
=(√6/4-√2/4)(√6/4+√2/4)
=6/16-2/16
=4/16
=1/4