Show that 1 – 2sin θ cos θ ≥ 0 for all θ ∈ R.

1.	Show that 1 – 2sin θ cos θ ≥ 0 for all θ ∈ R.
Answer» 1 – 2 sin θ cos θ = sin² θ + cos² θ – 2sin θ cos θ = (sin θ – cos θ)² ≥ 0 for all θ ∈ R

Answer»

1 – 2 sin θ cos θ

= sin² θ + cos² θ – 2sin θ cos θ

= (sin θ – cos θ)² ≥ 0 for all θ ∈ R

Discussion