Question

12.If sec θ + tan θ = 7, then evaluate sec θ – tan θ.​

Answer 1

The value of sec²θ + tan²θ is 3√5.

Explanation:

(secθ + tanθ)² = (7)²

sec²θ + tan²θ + 2•secθ•tanθ = 49. (as tanθ × cosθ = 1)

sec²θ + tan²θ +2 = 49

sec²θ + tan²θ = 49– 2

sec²θ + tan²θ = 47

Now,

(secθ – tanθ)² = sec²θ + tan²θ – 2•secθ•tanθ

(secθ – tanθ)² = 47 – 2

secθ – tanθ = √45

secθ – tanθ = 3√5