Question

If (sec θ – tan θ) = root 2 tan θ then prove that (sec θ + tan θ) = root 2 sec θ.

Answer 1

Answer:

Step-by-step explanation:

Let A = {θ : tan θ + sec θ = √2 sec θ} and B = {θ : sec θ - tan θ = √2 tan θ} be 2 sets. Then (1) A = B (2) A ⊂ B (3) A ≠ B (4) B ⊂ A

Solution: (1)

tan θ + sec θ = √2 sec θ

sin θ = √2 – 1

sec θ – tan θ = √2 tan θ

sin θ = 1 / (√2 + 1)

sin θ = √2 – 1

A = B