tan255°

=tan(180°+75°)

=tan75°

=tan(45°+30°)

=(tan45°+tan30°)/ ( 1-tan45°·tan30°)

=(1+√3/3)/ ( 1-1x √3/3)

=[(3+√3)/3)]/[(3-√3)/3]

=(3+√3)/(3-√3)

=(3+√3)?6

=(9+6√3+3)/6

=(12+6√3)/6

=6(2+√3)/6

=2+√3

≈3.73205

擴充套件資料

二倍角公式

sin2α=2sinαcosα

tan2α=2tanα/(1-tan^2(α))

cos2α=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)

半形公式

sin^2(α/2)=(1-cosα)/2

cos^2(α/2)=(1+cosα)/2

tan^2(α/2)=(1-cosα)/(1+cosα)

tan(α/2)=sinα/(1+cosα)=(1-cosα)/sinα