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sin^2x + cos^2x = 1
tgx = sinx / cosx; ctgx = cosx / sinx
1 + tg^2x = 1 / cos^2x
1 + ctg^2x = 1 / sin^2x
tgx = 1 / ctgx; ctgx = 1 / tgx
sin (x+y) = sinxcosy + sinycosx
sin (x-y) = sinxcosy - sinycosx
cos (x+y) = cosxcosy - sinxsiny
cos (x-y) = cosxcosy + sinxsiny
tg (x+y) = tgx+tgy / 1-tgxtgy
tg (x-y) = tgx-tgy / 1+ tgxtgy
sin2x = 2sinxcosx
cos2x = cos^2x - sin^2x = 2cos^2x -1 = 1 - 2sin^2x
tg2x = 1tgx / 1-tg^2x
sin (-x) = -sinx
cos (-x) = cosx
tg (-x) = -tgx
ctg (-x) = -ctgx
sinx + siny = 2sin(x+y)/2 * cos(x+y)/2
sinx - siny = 2sin(x+y)/2 * cos(x-y)/2
cosx+cosy = 2cos(x+y)/2 * cos(x+y)/2
cosx-cosy = -2sin(x-y)/2 * sin(x+y)/2 = 2sin(y-x)/2sin(y+x)/2