Question

Prove the following trigonometric identities:
cosθ/1-sinθ=1+sinθ/cosθ

Answer 1

Answer:

I am not sure about this answer

Answer 2

cosθ /(1 - sinθ) = (1 + sinθ) / cosθ . Proved

Step-by-step explanation:

To prove: cosθ /(1 - sinθ) = (1 + sinθ) / cosθ

Proof:  

cosθ /(1 - sinθ), multiplying both numerator and denominator by (1 + sinθ), we get:

cosθ /(1 - sinθ) = cosθ (1 + sinθ) / (1 + sinθ)(1 - sinθ)

= cosθ (1 + sinθ) / (1 - sin²θ

= cosθ (1 + sinθ) / cos²θ

= (1 + sinθ) / cosθ

Hence proved.