Question

Prove that :

Question 1 :

`(cos\theta - sin^2\theta +1)/(sin \theta(1+cos \theta )) = cot \theta`

Question 2:

`(tan\theta +sin \theta)/(tan\theta - sin\theta) =(sec\theta +1 )/(sec \theta -1)`

Answer 1

Please find attached herewith the solutions of your questions.

Hope it helps.

If you have any query, feel free to ask.

Answer 2

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)