求sin^10°+cos^40°+sin10°cos40°

运用余弦定理可得因为c^2=a^2+b^2-2abcosC运用正弦定理可得(2rsinC)^2=(2rsinA)^2+(2rsinB)^2-2(rsinA)(rsinB)cosC所以(sinC)^2=(sinA)^2+(sinB)^2-2sinAsinBcosC原式=sin^2(10°)+sin^2(50°)+sin10°sin50° =sin^2(10°)+sin^2(50°)-2sin10°sin50°cos120° =sin^2(120°) =3/4