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If x+iy=(1)/(1+ cos theta+ isin theta), ...

If `x+iy=(1)/(1+ cos theta+ isin theta)`, show that `4x^(2)-1=0`

Text Solution

Verified by Experts

The correct Answer is:
`4x^(2) = 1 => 4x^2 -1 = 0`
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Knowledge Check

  • If x + iy = (1)/((1 + cos theta + isin theta)) then sin^(-1) x =

    A
    `(pi)/(3)`
    B
    `(pi)/(4)`
    C
    `(pi)/(6)`
    D
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  • 1+ cos 2 theta + cos 4 theta + cos 6 theta =

    A
    `4 sin theta * sin 2 theta * sin 3theta `
    B
    `4 cos theta * cos 2 theta * cos 3 theta `
    C
    `4 tan theta * tan 2 theta * tan 3 theta `
    D
    `4 cot theta * cot 2 theta * cot 3 theta `

  • If (1 + cos theta + isin theta) (1 + cos 2 theta + isin 2theta) = x + iy then y =

    A
    `x tan ((3theta)/(2))`
    B
    `x tan ((5theta)/(2))`
    C
    `x tan((7theta)/(2))`
    D
    `x tan ((9theta)/(2))`

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    If x = cos theta (1 + cos theta ), y = sin theta (1 + cos theta ) show that ((dy)/(dx)) _(theta = ( pi )/(2)) =1.

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