ZJSG09112007
contestada

Prove that :
Question 1 :
[tex]\frac{cos\theta - sin^2\theta +1}{sin \theta(1+cos \theta )} = cot \theta[/tex]

Question 2:
[tex]\frac{tan\theta +sin \theta}{tan\theta - sin\theta} =\frac{sec\theta +1 }{sec \theta -1}[/tex]

Respuesta :

mhanifa

Answer:

Identities used

  • sin²θ + cos²θ = 1
  • cosθ / sinθ = cotθ
  • sinθ/cosθ = tanθ
  • 1/cosθ = secθ

Question 1

  • (cosθ - sin²θ + 1) / sinθ(1 + cosθ) =
  • (cosθ + cos²θ) / sinθ(1 + cosθ) =
  • cosθ(1 + cosθ) / sinθ(1 + cosθ) =
  • cosθ / sinθ =
  • cotθ

Question 2

  • (tanθ + sinθ) / (tanθ - sinθ) =
  • (sinθ/cosθ + sinθ) / (sinθ/cosθ - sinθ) =
  • sinθ(1/cosθ + 1) / sinθ(1/cosθ - 1) =
  • (1/cosθ + 1) / (1/cosθ - 1) =
  • (secθ + 1) / (secθ - 1)