sin285°-cos105°=

sin285°-cos105°
=sin(270°+15°)-cos(90°+15°)
=-cos15°+sin15°
=√2(sin15°cos45°-cos15°sin45°)
=√2sin(15°-45°)
=√2sin(-30°)
=-√2/2

负二分之根号2
sin285-cos105=
--sin105--cos105=--根号2sin(105+45)=负二分之根号2

=sin285+sin15
=2sin150cos135
=cos135
=负二分之根号2

sin(180+105)-cos105
=sin105-cos105
=√2 sin（105+45）
=√2sin150
= -√2

sin285=sin(360-75)=sin75。cos105=cos(180-75)=-cos75。所以原题等于sin75+cos75,又sin75=sin(45+30)=√2／2×√3／2+√2／2×1／2=(√6＋√2)／4。cos75=cos(45+30)=√2／2×√3／2－√2／2×1／2＝(√6－√2)／4。所以原式＝(√6＋√2＋√6－√2)／4＝√6／2