| sin (2α) = 2 . sin α . cosα | . . | ⁄sin (α/2)/ = √[(1-cosα) / 2] |
cos (2α) = cos2α - sin2α = = 2 . cos2α - 1 | | /cos (α/2)/ = √[(1+cosα) / 2] |
| tg (2α) = 2 tgα / (1 - tg2α) | | /tg (α/2)/ = √[(1-cosα) / (1+cosα)] |
| tg (2α) = 2 / (cotgα - tgα) | | tg (α/2) = (1 - cos α) / sinα = = sin α / (1 + cosα) |
cotg (2α) = (cotg2α - 1) / (2.cotgα) = = ½(cotg α - tgα) | | /cotg (α/2)/ = √[(1+cosα) / (1-cosα)] |
| | | cotg (α/2) = (1+cosα) / sinα |
| | | |
| sinα = 2 . sin(α/2) . cos (α/2) | | /sinα/ = √[½{1-cos(2α)}] |
cosα = cos2(α/2) - sin2(α/2)= = 1 - 2sin2(α/2) = 2cos2(α/2) - 1 | | /cosα/ = √[½{1+cos(2α)}] |
tgα = 2tg(α/2) / [1 - tg2(α/2)] = = 2/[cotg(α/2) - tg(α/2)] | | /tgα/ = √{[1-cos(2α)] / [1+cos(2α)]} |
| | | tgα = sin(2α)/[1 + cos(2α)] = = [1 - cos(2α)] / sin(2α) |
cotgα = [cotg2(α/2) - 1] / [2 cotg (α/2)] = = ½ [cotg(α/2) - tg(α/2)] | | /cotgα/ = √{[1+cos(2α)] / [1-cos(2α)]} |
| | | cotgα = sin(2α) / [1 - cos(2α)] = = [1 + cos(2α)] / sin(2α) |
sin(3α) = 3 sinα - 4 sin3α
sin(4α) = 8 sinα cos3α - 4 sinα cosα
sin(5α) = 16 sinα cos4α - 12 sinα cos2α + sinα
| sin (nα) = n sinα cosn-1α | - ( | n | ) sin3α cosn-3α | + ( | n | ) sin5α cosn-5α - .... |
| 3 | 5 |
cos(3α) = 4 cos3α - 3 cosα
cos(4α) = 8 cos4α -8 cos2α + 1
cos(5α) = 16 cos5α - 20 cos3α + 5 cosα
| sin (nα) = cosnα | - ( | n | ) sin2α cosn-2α | + ( | n | ) sin4α cosn-4α - .... |
| 2 | 4 |
tg(3α) = [3 tgα - tg3α] / [1-3tg2α]
tg(4α) = [4 tgα - 4tg3α] / [1 - 6tg2α + tg4α]
| tg (nα) = [n tgα | - ( | n | ) tg3α | + ( | n | ) tg5α - ....] |
| 3 | 5 |
/
| [ 1 | - ( | n | ) tg2α | + ( | n | ) tg4α - ( | n | ) tg6α + ....] |
| 2 | 4 | 6 |
cotg(3α) = [cotg3α - 3cotgα] / [3cotg2α - 1]
cotg(4α) = [cotg4α - 6cotg2α + 1] / [4cotg3α - 4cotgα]
| cotg (nα) = [cotgnα | - ( | n | ) cotgn-2α | + ( | n | ) cotgn-4α - ....] |
| 2 | 4 |
/
| [n cotgn-1α | - ( | n | ) tg2α | + ( | n | ) cotgn-3α - ( | n | ) cot6n-5α - ....] |
| 3 | 4 | 5 |