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If n is an integer and z=cis theta,(thet...

If n is an integer and `z=cis theta,(theta ne (2n+1)pi/2),` then show that `(z^(2n)-1)/(z^(2n)+1)=i tan n theta)`.

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Knowledge Check

  • If z=cos theta+isintheta then (z^(2n)-1)/(z^(2n)+1)=

    A
    `cos n theta`
    B
    `sin n theta`
    C
    `-i sin" "n" "theta`
    D
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  • If n (ne 3) is an integer and z = -1 + isqrt3 , then z^(2n) + 2^(n) , z^(n) + 2^(2n) =

    A
    `0`
    B
    `2`
    C
    `3`
    D
    `4`

  • If |2 sin theta - cos ec theta| ge 1 and theta ne (n pi)/(2), n in Z , then

    A
    `cos 2 theta ge 1//2`
    B
    `cos 2 theta ge 1//4`
    C
    `cos 2 theta le 1//2`
    D
    `cos 2 theta le 1//4`

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