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