Question

The maximum value of Δ = `|(1, 1, 1),(1, 1 + sin theta, 1),(1 + cos theta, 1, 1)|` is ______. (θ is real number)

Options

• `1/2`

• `sqrt(3)/2`

• `sqrt(2)`

• `(2sqrt(3))/4`

Answer 1

The maximum value of Δ = `|(1, 1, 1),(1, 1 + sin theta, 1),(1 + cos theta, 1, 1)|` is `1/2`. (θ is real number)

Explanation:

Δ = `|(1, 1, 1),(1, 1 + sin theta, 1),(1 + cos theta, 1, 1)|`

[Applying C₁ → C₁ – C₁ and C₂ → C₂ – C₃]

= `|(0, 0, 1),(0, sin theta, 1),(cos theta, 0, 1)|`

= – sin θ · cos θ

= `-1/2 * 2 sin theta cos theta`

= `- 1/2 sin 2theta`

So, maximum value of Δ is `1/2` when sin 2θ = –1.