不查表求值sin²10°+cos²40°+sin10°cos40° 请有具体的解题过程,

原式 = (1 - cos20°)/2 + (1 + cos80°)/2 + sin10°cos40° (利用二倍角公式)
= 1 + (cos80° - cos20°)/2 + [sin(10° + 40°) + sin(10° - 40°)]/2 (利用积化和差公式)
= 1 + (cos80° - cos20°)/2 + [sin50° + sin(-30°)]/2 (利用和差化积公式)
= 1 - 2{sin[(80°+20°)/2] sin[(80° - 20°)/2]}/2+ (sin50° -1/2)/2
= 1 - sin50° sin30° + (sin50°)/2 -1/4
= 1 - (sin50°)/2 + (sin50°)/2 - 1/4
= 3/4