If cos θ = 2/3 then 2 sec 2 θ + 2tan 2 θ – 4 is equal to

Question

Philoid · Accepted Answer

Given,

cos θ = 2/3 = b/h = k

2sec² θ + 2 tan²θ – 7

b = 2k, h = 3k

In ∆ABC,

h² = p² + b²

⇒ (3k)² = p² + (2k)²

⇒ 9k² = p² + 4k²

⇒ p² = 9k² – 4k²

⇒ p² = 5k²

⇒ p = √5k

Then,

Sec θ = h/b = 3k/2k = 3/2 and

Tan θ = p/b = √5k/2k = √5/2

⇒ 2 sec² θ + 2 tan² θ – 7

⇒