三角形正弦余弦求值cos78度sin42度＋sin78度sin48度＝?

cos78度sin42度＋sin78度sin48度＝cos78度sin42度＋sin78度cos48度＝sin(78+42)=sin120°=根号3/2

=cos(90-12)sin(30+12)+sin(90-12)sin(60-12)
=sin12(sin30cos12+cos30sin12)+cos12(sin60cos12-cos60sin12)
=sin30sin12cos12+cos30sin12sin12+sin60cos12cos12-cos60sin12cos12
=(sin30sin12cos12-cos60sin12cos12)+cos30sin12sin12+sin60cos12cos12
=(sin30sin12cos12-sin30sin12cos12)+sin60sin12sin12+sin60cos12cos12
=0+sin60=根号3/2
因为不好打根号...一直用sin30 cos60表示。 你一开始就写出他们的值 会看的更明白些

和差角公式上

cos78度sin42度＋sin78度sin48度
=cos78度sin42度＋sin78度cos42度
=sin(78+42)
=sin120
=√3/2

解；
∵sin48=sin(90-42)=cos42
∴cos78度sin42度＋sin78度sin48度
=cos78度sin42度＋sin78度cos42
=sin(42+78)
=sin120
=√3/2