Integrales Trigonometricas Formulas
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sen 2 x + cos 2 x = 1 1 + tag 2 x = sec 2 x 1 + cot 2 x = csc 2 x sen 2 x = 1/2(1 - cos2x) cos 2 x = 1/2(1 + cos2x) senx cosx = 1/2sen2x senx cosy = 1/2[sen(x - y) + sen(x + y)] senx seny = 1/2[cos(x - y) - cos(x + y)] cosx cosy = 1/2[cos(x - y) + cos(x + y)] 1 - cosx = 2sen 2 1/2x 1 + cosx = 2cos 2 1/2x 1 + sen x = 1 + cos(1/2 - x) 1 - sen x = 1 - cos(1/2 - x) Especialmente importantes son estas dos identidades: sen x = (2 tan(x/2))/(1 + tan 2 (x/2)) cos x = (1 - tan 2 (x/2))/(1 + tan 2 (x/2)) Haciendo t = tan x/2, nos queda: sen x = 2t/(1 + t 2 ) cos x = (1 - t 2 )/(1 + t 2 ) dx = 2 dt/(1 + t 2 )
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Transcript of Integrales Trigonometricas Formulas
sen2x + cos2x = 11 + tag2x = sec2x1 + cot2x = csc2xsen2x = 1/2(1 - cos2x)cos2x = 1/2(1 + cos2x)senx cosx = 1/2sen2xsenx cosy = 1/2[sen(x - y) + sen(x + y)]senx seny = 1/2[cos(x - y) - cos(x + y)]cosx cosy = 1/2[cos(x - y) + cos(x + y)]1 - cosx = 2sen21/2x1 + cosx = 2cos21/2x1 + sen x = 1 + cos(1/2 - x)1 - sen x = 1 - cos(1/2 - x)
Especialmente importantes son estas dos identidades:sen x = (2 tan(x/2))/(1 + tan2(x/2))cos x = (1 - tan2(x/2))/(1 + tan2(x/2))
Haciendo t = tan x/2, nos queda:
sen x = 2t/(1 + t2)cos x = (1 - t2)/(1 + t2)dx = 2 dt/(1 + t2)
