Question

If `sin θ - cos θ = 3/5`, then sin θ cos θ = ______.

Answer 1

If `sin θ - cos θ = 3/5`, then sin θ cos θ = `underlinebb(8/25)`.

Explanation:

Square both sides: `(sin θ - cos θ)^2 = (3/5)^2 = 9/25`.

But (sin θ – cos θ)² = sin² θ + cos² θ – 2 sin θ cos θ 

= 1 – 2 sin θ cos θ

So `1 - 2 sin θ cos θ = 9/25` 

⇒ `2 sin θ cos θ = 16/25` 

⇒ `sin θ cos θ = 8/25`