State True or False for the statements

The maximum value of is 1/2.

True

Given

Performing operations R₂→ R₂ – R₁ and R₃→ R₃ – R₁

= cos θ. sin 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

Hence the above statement is true.