Prove that : Question 1 :

Question 2:

Identities used

sin²θ + cos²θ = 1cosθ / sinθ = cotθsinθ/cosθ = tanθ1/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)

Chope that