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Prove that the determinant {:[( x, sin ...

Prove that the determinant ` {:[( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) ]:}` is independent of ` theta.

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Knowledge Check

  • ((1+ sin theta - cos theta )/( 1+ sin theta + cos theta ))^(2)=

    A
    `(1+ cos theta )/(1- cos theta ) `
    B
    `(1- cos theta)/(1+ cos theta ) `
    C
    `(1+ sin theta )/( 1- sin theta ) `
    D
    `(1- sin theta )/(1+ sin theta ) `
  • ( sin 3 theta )/( sin theta ) -(cos 3 theta )/( cos theta )=

    A
    `2`
    B
    `sqrt(3)`
    C
    `sqrt(2)`
    D
    1
  • sin theta=cos theta,theta in Q_1 then theta -

    A
    `(pi^e)/(2)`
    B
    `(pi^e)/(3)`
    C
    `(2pi^e)/(4)`
    D
    `(pi^e)/(4)`
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