If , then find the values of cos θ and .

We know that,

Or,

Let,

Side opposite to angle θ = AB = x² – y²

and Hypotenuse = AC = x² + y²

In right angled ∆ABC, we have

(AB)² + (BC)² = (AC)² [by using Pythagoras theorem]

⇒ (x² – y² )² + (BC)² = (x² + y² )²

⇒ (BC)² = (x² + y² )² – (x² – y² )²

Using the identity, a² – b² = (a+b)(a – b)

⇒ (BC)² = [(x² + y² + x² – y² )][ x² + y² –( x² – y²)]

⇒ (BC)² = (2x²)(2y²)

⇒ (BC)² = (4x²y²)

⇒ BC =√4x²y²

⇒ BC = ±2xy

⇒ BC = 2xy [taking positive square root since, side cannot be negative]

and

So,