sin(50度)*cos(10度)+sin(40度)*sin(10度)=

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sin(50度)*cos(10度)+sin(40度)*sin(10度)=
sin(50度)*cos(10度)+sin(40度)*sin(10度)=

sin(50度)*cos(10度)+sin(40度)*sin(10度)=
sin(50度)*cos(10度)+sin(40度)*sin(10度)
=sin(50度)*cos(10度)+sin(90度-50度)sin(10度)
=sin(50度)*cos(10度)+cos(50度)sin(10度)
=sin(50度+10度)
=sin60度
=√3/2

直接展开就行,下面就不写角度了,直接写数,实际上是角度:
sin50 * cos10 + sin40 * sin10
= 1/2 (sin60 + sin40) - 1/2 (cos50 - cos30)
(这里sin40 = cos50
继续...)
= 1/2 (sin60 + cos30)
= (根号3) / 2