1 / 12

sen 2 x + cos 2 x = 1

Clase 64. Ejercicios sobre Identidades trigonométricas. sen 2 x + cos 2 x = 1. Revisión del estudio individual. Demuestra las siguientes identidades para los valores admisibles de la variable. 1. a) tan x • sen x+cos x =. cos x. b) (1 – sen 2 )(1 +tan 2  ) = 1.

charla
Télécharger la présentation

sen 2 x + cos 2 x = 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Clase 64 Ejercicios sobre Identidades trigonométricas sen2x + cos2x = 1

  2. Revisión del estudio individual Demuestra las siguientes identidades para los valores admisibles de la variable. 1 a) tan x • sen x+cos x = cos x b) (1 – sen2)(1 +tan2 )= 1 sen x • cot x+cos x c) = 2sen x cot x

  3. 1 sen x •sen x + cos x = cos x 1 = cos x M.D: cos x tan x • sen x + cos x 1 sen2 x + cos2x = cos x Se cumple

  4. 1 1 + tan2  = cos2 1 cos2 b) (1 – sen2)(1 +tan2 )= 1 (1 – sen2)(1 + tan2 ) cos2 = cos2x = 1 M.D: 1 Lo que queda demostrado

  5. 2sen x sen x • cot x+cos x cot x sen x •cot x cos x = + cot x cot x cosx: cotx sen x =sen x + = cos x sen x = 2 sen x cos x = sen x L.q.q.d

  6. sen x cos x tan x = cot x = cos x sen x 1 1 1 + cot2x = 1 + tan2x = sen2x cos2x Identidades básicas sen2x = 1 – cos2x sen2x + cos2x = 1 cos2x = 1 – sen2x tan x • cot x = 1

  7. cos x 1 1 + = sen2x sen2x 1 + cos x Ejercicios: • Prueba, la validez de las siguientes igualdades para los valores admisibles de la variable x.

  8. A cos x 1 1 + = B sen2x sen2x 1 + cos x = AK BK = 1 = = (1 + cos x) (1 + cos x) (1 + cos x) sen2x sen2x sen2x sen2x sen2x + cos x(1 + cos x) sen2x + cos x + cos2x sen2x cos2x 1 + cos x L.q.q.d

  9. 2 1 1 1 – sen x 1 + sen x 2 + = x (2k+1) cos2 x • Demuestra las siguientes identidades: 1 + sen2x 2 a) – cos x = cos x cos x b)

  10. 1 + sen2 x = cos x 1 + sen2x 2 – cos x = cos x cos x 2– cos2 x = cos x 2–( 1 – sen2x) = cos x 2 – 1 + sen2x = cos x Se cumple

  11. 1 1 1 1 1 – sen x 1 – sen x 1 + sen x 1 + sen x 2 2 + + = = 1 – sen2x cos2 x 2 b) = cos2 x 1+ sen x + 1 – senx = 1 – sen2x 1 – sen2x = cos2x l.q.q.d

  12. 2 cos2x –1 +sen2x cot2x = 1 –cos2x 2 senx.cosx – senx senx = 2cosx + 1 – 4sen2x +3 Para el estudio individual Prueba que para los valores admisibles de la variable se cumple: a) b)

More Related