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Find the determinant of  . 

  1. 1
  2. xsin2θ 
  3. x2
  4. -x3

Answer (Detailed Solution Below)

Option 4 : -x3
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Detailed Solution

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Concept :

A=  

Then determinant of matrix A , | A | = = a11 × {(a22 × a33) – (a23 × a32)} - a12 × {(a21 × a33) – (a23 × a31)} + a13 × {(a21 × a32) – (a22 × a31)} . 

Calculation:

⇒ Δ =  

⇒ Δ =  

⇒ Δ =  

⇒ Δ =                

⇒ Δ = - x3                                        [∵ sin2 θ + cos2 θ = 1]

The correct option is 4.

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