English Version 中文版 日本語版   » Group 1 sin(α ± β) = sin α · cos β ± cos α · sin β   cos(α ± β) = cos α · cos βsin α · sin β   tg(α ± β) = tg α ± tg β   1 tg α · tg β     Group 2 sin α · cos β = ½[sin(α - β) + sin(α + β)]   sin α · sin β = ½[cos(α - β) - cos(α + β)]   cos α · cos β = ½[cos(α - β) + cos(α + β)]   Group 3 sin α + sin β = 2·[sin((α + β)/2)·cos((α - β)/2)]   sin α - sin β = 2·[cos((α + β)/2)·sin((α - β)/2)]   cos α + cos β = 2·[cos((α + β)/2)·cos((α - β)/2)]   cos α - cos β = - 2·[sin((α + β)/2)·sin((α - β)/2)]   Group 4 sin 2α = 2 sin α · cos α   cos 2α = cos2α - sin2α = 2 cos2α - 1 = 1- 2 sin2α   tg 2α = 2 tg α   1 - tg2α     sin 3α = 3 sin α - 4 sin3α   cos 3α = 4 cos3α - 3 cos α   tg 3α = 3 tg α - tg3α   1 - 3 tg2α     Group 5 sin α = 2 tg(α/2)   1 + tg2(α/2)     cos α = 1 - tg2(α/2)   1 + tg2(α/2)     tg α = 2 tg(α/2)   1 - tg2(α/2)     Group 6 sin(arcsin x) = x ( |x| ≤ 1 )   sin(arccos x) =   1 - x2 ( |x| ≤ 1 )   sin(arctg x) = x   1 + x2     sin(arcctg x) = 1   1 + x2     cos(arcsin x) =   1 - x2 ( |x| ≤ 1 )   cos(arccos x) = x ( |x| ≤ 1 )   cos(arctg x) = 1   1 + x2     cos(arcctg x) = x   1 + x2     tg(arcsin x) = x ( |x| ≤ 1 ) 1 - x2     tg(arccos x) =   1 - x2   ( |x| ≤ 1 ) x   tg(arctg x) = x     tg(arcctg x) = 1/x