Question

Prove that tan² θ – (1/cos² θ) + 1 = 0

Answer 1

Tan² θ – (1/cos² θ) + 1 = 0

Explanation:

Given: Tan² θ – (1/cos² θ) + 1 = 0

From trigonometric identities, we know that sec² θ = 1/cos² θ, sec² θ = 1 + tan² θ  

Tan² θ – (1/cos² θ) + 1 = 0

tan² θ – sec² θ + 1 = 0

(1 + tan² θ) – sec² θ = 0

sec² θ - sec² θ = 0

0 = 0

Hence proved.