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Find the general value of theta from the...

Find the general value of `theta` from the equation `costheta+cos2theta + cos3theta=0`.

Text Solution

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`costheta+cos2theta+cos3theta=0`
`rArr cos3theta+costheta+cos2theta=0`
`rArr cos2theta(2costheta+1)=0`
`rArr cos2theta=0` or `2costheta+1=0`
Now, `cos2theta=0`
`rArr 2theta=(2n+1)pi/2`.
`=cos(pi-pi/3)=cos(2pi)/(3)`
`rArr theta=2npi+-(2pi)/(3)`. Ans.
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Knowledge Check

  • The general value theta obtained from the equation cos3theta=sinalpha is

    A
    `2theta=(pi)/(2)-alpha`
    B
    `theta=2npipm((pi)/(2)-alpha)`
    C
    `theta=(npi+(-1)^(n)alpha)/(2)`
    D
    `theta=2npi/3pm((pi)/(6)-(alpha)/(3))`

  • The general value of theta which satisfies the equation (costheta+isintheta)(cos3theta+isin3theta) (cos5theta+isin5theta)…………((cos2n-1)theta+isin(2n-1)theta) = 1 is

    A
    `(rpi)/n^(2)`
    B
    `((r-1)pi)/(n^(2))`
    C
    `((2r+1)pi)/(n^(3))`
    D
    `(2rpi)/n^(2)`

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