Question

The maximum value of `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|` is `1/2`

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let Δ = `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|`

C₁ → C₁ – C₂, C₂ → C₂ – C₃

= `|(0, 0, 1),(-sintheta, sintheta, 1),(0, -costheta, 1 + costheta)|`

Expanding along C₃

= `1|(-sintheta, sintheta),(0, -costheta)|`

= sin θ cos θ – 0

= sin θ cos θ

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

= `1/2 sin 2theta`

= `1/2 xx 1`  ......[Maximum value of sin 2θ = 1]

= `1/2`