Question

Prove the following trigonometric identities:
1+sinθ/cosθ+cosθ/1+sinθ=2secθ

Answer 1

Answer:

L.H.S =R.H.S

Hope it helps you

Answer 2

1 + sin θ / cos θ + cos θ / 1 + sin θ = 2 sec θ  proved

Step-by-step explanation:

To prove: 1 + sin θ / cos θ + cos θ / 1 + sin θ = 2 sec θ

Proof:  

(1 + sin θ) / cos θ + cos θ / (1 + sin θ) = (1 + sin θ)²/ cos θ (1 + sin θ) + Cos² θ / cos θ (1 + sin θ)

 = (1 + Sin² θ + 2.Sin θ + Cos² θ) / cos θ (1 + sin θ)

 = (1 + 1 + 2. Sin θ) / cos θ (1 + sin θ)

 = 2 (1 + sin θ) / cos θ (1 + sin θ)

 = 2 / cos θ

= 2 Sec θ

Hence proved.