The maximum value of is (θ is a real number)

Given

Performing operations C₁→ C₂ – C₃ and C₂→ C₂ – C₃

= 0 – 0 + 1 (sin θ. cos θ)

Multiply and divide by 2,

= 1/2 (2sin θ cos θ)

We know that 2 sin θ cos θ = sin 2θ

= 1/2 (sin 2θ)

Since the maximum value of sin 2θ is 1, θ = 45°.

∴ Δ = 1/2 (sin 2(45°))

= 1/2 sin 90°

= 1/2 (1)

∴ Δ = 1/2