一,sin^4a+cos^4a
=(sin²a+cos²a)²-2sin²acos²a
=1-(1/2)(2sinacosa)²
=1-(1/2)sin²2a
二：sin10°*cos20°*cos40°
=cos10°sin10°*cos20°*cos40°/cos10°
=(1/2)sin20°*cos20°*cos40°/cos10°
=(1/4)sin40°*cos40°/cos10°
=(1/8)sin80°/cos10°
=(1/8)cos10°/cos10°
=1/8