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The determinant Delta=|{:(cos(x+y),-sin(...

The determinant `Delta=|{:(cos(x+y),-sin(x+y),cos2y),(sinx,cosx,siny),(-cosx,sinx,cosy):}|` is independent of x only.

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Knowledge Check

  • If x,y in R then the determinant Delta=|{:(cosx,-sinx,1),(sinx,cosx,1),(cos(x+y),-sin(x+y),0):}| lies in the interval

    A
    `[-sqrt(2),sqrt(2)]`
    B
    `[-1,1]`
    C
    `[-sqrt(2),1]`
    D
    `[-1,-sqrt(2)]`

  • The number of distinct real roots of |{:(sinx,cosx,cosx),(cosx,sinx,cosx),(cosx,cosx,sinx):}|=0 in the interval -(pi)/(4) le x le (pi)/(4) is

    A
    `0`
    B
    `2`
    C
    `1`
    D
    `3`

  • inte^x(cosx- sinx)dx=

    A
    `-e^xcos+C`
    B
    `e^xsinx+C`
    C
    `-e^xcos+C`
    D
    `e^xcosx+C`

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    If Delta (x)=|{:(1,cos x,1-cos x),(1+sin x,cos x,1+sinx-cosx),(sinx,sinx,1):}| then int_(0)^(pi//2)Delta(x) dx is equal to

    If f(x) =|{:(sinx,cosx,sinx),(cosx,-sinx,cosx),(x,1,1):}| find the value of 2[f'(0)]+[f'(1)]^(2)

    If Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1+x),e^(x),sinx),(cosx,tanx,sin^(2)x):}| then

    If y=(sinx)^(cosx) + (cos x)^sinx , then find dy/dx .

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