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Prove that int0^(pi/2)(costheta-sintheta...

Prove that `int_0^(pi/2)(costheta-sintheta)/(1+sintheta.costheta)d theta=0.`

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Knowledge Check

  • If A = ((costheta,-sintheta),(sintheta,costheta)) then

    A
    A is an orthogonal matrix
    B
    A is a symmetric matrix
    C
    A is a skew -symmetric matrix
    D
    none of these

  • (sintheta-costheta+1)/(sintheta+costheta-1) is equal to

    A
    `(1)/(tan theta - sec theta)`
    B
    `(1)/(sec theta - tan theta)`
    C
    `(1)/(cos theta - tan theta)`
    D
    `(1)/(tan theta - cos theta)`

  • If A=[(costheta,-sintheta),(sintheta,costheta)] " then " A^(-1) =?

    A
    A
    B
    `-A`
    C
    adjA
    D
    `=-adjA`

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    Evaluate the following integral: int_0^(pi//2)(sintheta)/(sqrt(1+costheta))d theta

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