Question

大家来帮帮我吧,数学题...我想了1个多小时了求(cos24)^2+(sin6)^2+(cos18)^2

求(cos24)^2+(sin6)^2+(cos18)^2

Answer 1

sin18°=(根号5-1)/4（必须公式）
原式＝(cos24)^2+1-(cos6)^2+(cos18)^2
＝(1＋cos48-1-cos12+1+cos36）/2+1
＝(cos48-cos12+1+cos36)/2+1
＝[cos(60-12)-cos12+cos36+1〕/2+1
＝[1/2cos12+根号3/2sin12-cos12+cos36+1〕/2+1
＝[根号3/2sin12-1/2cos12+cos36+1〕/2+1
＝[sin(12-30)+cos36+1〕/2+1
＝[-sin18+cos36+1〕/2+1
＝[-sin18+(cos18)^2-(sin18)^2+1]/2+1
＝[-sin18+1-2(sin18)^2 +1]/2+1
代入 sin18°=(根号5-1)/4，即可得原式＝1.75