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Solve |[y,sinx,cosx] , [cosx,1,y] , [-si...

Solve `|[y,sinx,cosx] , [cosx,1,y] , [-sinx,-y,1]|`

Answer

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Knowledge Check

  • If |[cosx, sinx, cosx], [-sinx, cosx, sinx], [-cosx, -sinx, cosx]|=0 , then x=

    A
    `(2n+1)(pi)/(2), ninZ`
    B
    `(2n+1)(3pi)/(2), ninZ`
    C
    `(2n+1)(pi)/(4), ninZ`
    D
    `(2n+1)pi, ninZ`

  • If x,y inR , then the determinant Delta=|(cosx,-sinx,1),(sinx,cosx,1),(cos(x+y),-sin(x+y),0)| in the interval

    A
    `[-sqrt2,sqrt2]`
    B
    `[-1,1]`
    C
    `[-sqrt2,1]`
    D
    `[-1,-sqrt2]`

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    Solve: sinx+cosx=(sqrt3+1)/4

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    F(x)=[[cosx,-sinx,0],[sinx,cosx,0],[0,0,1]] and G(x)=[[cosx,0,sinx],[0,1,0],[-sinx,0,cosx]], then [F(x)G(y)]^(-1) is equal to (A) F(-x)G(-y) (B) F(x-1)G(y-1) (C) G(-y)F(-x) (D) G(y^(-1))F(x^(-1))

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