Question

If cos2θ = 0, then `|(0, costheta, sin theta),(cos theta, sin theta,0),(sin theta, 0, cos theta)|^2` = ______.

Answer 1

If cos2θ = 0, then `|(0, costheta, sin theta),(cos theta, sin theta,0),(sin theta, 0, cos theta)|^2` = `- 1/sqrt(2)`.

Explanation:

Δ = `|(0, costheta, sin theta),(cos theta, sin theta,0),(sin theta, 0, cos theta)|^2`

 = `0 - cos theta(costheta) + sintheta(0- sin^2theta)`

= `-(cos^3theta + sin^2theta)`

cos2θ = 0

⇒ 2θ = `pi/2`

⇒ θ = `pi/4`

∴ Δ = `-(cos^3  pi/4 + sin^3  pi/4)`

= `-((1/sqrt(2))^3 +(1/sqrt(2))^3)`

=`- 1/sqrt(2)`