sin165°cos75°+cos15°sin105°等于?

原式=sin(180-15)cos75+cos75sin(180-75)
-sin15cos75+cos75sin75
=sin(15+75)
=sin90
=1

sin165°cos75°+cos15°sin105°
=sin15°sin15°+cos15°cos15°
=1

原式=sin(180-15)cos75+cos75sin(180-75)
-sin15cos75+cos75sin75
=sin(15+75)
=sin90
=1

sin165cos75+cos15sin105
=sin(90+75)cos75+cos(60-45)sin(60+45)
=cos75cos75+(cos60cos45+sin60sin45)(sin60cos45+cos60sin45)
=cos(45+30)cos75+(√2/4+√6/4)(√6/4+√2/4)
=(cos45cos30-sin45sin30)cos75+3/8+1/8+√3/4
=(√6/4-√2/4)^2+1/2+√3/4
=3/8-√3/4+1/8+1/2+√3/4
=1