數學..和差化積

cos10° cos30° cos50° cos70°= (√3/2) cos10° cos50° cos70°= (√3/2) (1/2)[cos(50+10)° + cos(50-10)°] cos70°= (√3/4) (cos60° + cos40°) cos70°= (√3/4) (1/2 + cos40°) cos70°= (√3/8)cos70° + (√3/4)cos40°cos70°= (√3/8)cos70° + (√3/4)(1/2)[cos(70+40)° + cos(70-40)°]= (√3/8)cos70° + (√3/8)(cos110° + cos30°)= (√3/8)cos70° + (√3/8)(cos110° + √3/2)= (√3/8)cos70° + (√3/8)cos110° + 3/16= (√3/8)cos70° - (√3/8)cos(180-110)° + 3/16= 3/16