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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