Question

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

Answer 1

Step-by-step explanation:

please mark me.as brainliest

Answer 2

(1 + Sinθ) / Cosθ = 1+cosθ+sinθ / 1+cosθ-sinθ  proved

Step-by-step explanation:

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

Proof:  

Cos²θ = 1 - Sin²θ

Cosθ. Cosθ = (1 - Sinθ) (1 + Sinθ)

Cosθ / (1 - Sinθ) =  (1 + Sinθ) / Cosθ = [Cosθ + (1 + Sinθ)] / [(1 - Sinθ) + Cosθ] from the theorem on equal ratios.

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

RHS = LHS

Hence proved.