求sin^2 40°+cos^2 10°-sin40°sin80°的值.
2个回答

用到积化和差公式和倍角公式

sinαsinβ=-[cos(α+β)-cos(α-β)]/2

cos^2 α=1/2(1+cos2α)

sin^2 40°+cos^2 10°-sin40°sin80°

=cos^2 50°+cos^2 10°+1/2[cos (40°+80°)-cos(40°-80°)

=1/2(1+cos100°)+1/2(1+cos20°)+1/2[cos (40°+80°)-cos(40°-80°)

=1+1/2(cos100°+cos20°)+1/2(cos120°-cos40°)

=1+1/2(cos100°+cos20°)-1/4-1/2cos40°

=3/4+cos60°cos40°-1/2cos40°

=3/4