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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.

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sen 2 x + cos 2 x = 1

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  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)

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