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If sin theta.sin (60+theta)sin (60-theta...

If `sin theta.sin (60+theta)sin (60-theta)=1//4` then `theta =`

A

`n pi` or `(3n pm 1) (pi)/(9) : n in Z`

B

`(n pi)/(3)+(-1)^(n)(pi)/(6) : n in Z`

C

`(2n pi)/(3)pm(pi)/(9) : n in Z`

D

`(n pi)/(3)+(pi)/(18).n in Z`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • sin 4 theta * sin 6 theta =

    A
    `1/2[ cos 2 theta - cos 10 theta ]`
    B
    `1/2[ cos 2 theta + cos 10 theta ]`
    C
    `1/2[ sin theta - cos 10 theta ]`
    D
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  • If cos^(2)theta - sin theta = 1//4 then theta =

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    `n pi + (-1)^(n)(pi)/(4) : n in Z`
    B
    `n pi + (-1)^(n)(pi)/(6) : n in Z`
    C
    `n pi + (-1)^(n+1)(pi)/(6) : n in Z` or `n pi +(-1)^(n)(pi)/(3) : n in Z`
    D
    `n pi + (-1)^(n)(pi)/(2) : n in Z` or `n pi +(-1)^(n)(pi)/(6) : n in Z`

  • If sin^(3) theta cos theta - cos ^(3) theta sin theta = 1 //4 " then " theta =

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    `theta = (n pi)/( 2) + (pi)/(8) n in Z`
    B
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    C
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    D
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