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If x sin theta = y sin ( theta + (2pi)/3...

`If x sin theta = y sin ( theta + (2pi)/3) = z sin ( theta+ (4pi)/3),` then the value of xy+yz+zx will be-

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Knowledge Check

  • If sin 6 theta =32 cos ^(5) theta sin theta -32 cos ^(3) theta sin theta + 3x, then the value of x is-

    A
    `cos theta`
    B
    `sin theta`
    C
    `sin 2 theta`
    D
    `cos 2 theta`

  • If tan theta =-4/3, then the value of sin theta is -

    A
    `2/5`
    B
    `4/5 or , -4/5`
    C
    `4/5 but ne -4/5`
    D
    `-4/5 but ne 4/5`

  • If sin theta =12/13 (0 lt theta lt (pi)/(2)) and cos phi =-3/5 (pi lt phi lt (3pi)/(2)) then the value of sin (theta+ phi) will be-

    A
    `1/65`
    B
    `56/65`
    C
    `-1/65`
    D
    `-56/65`

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    If theta + emptyset = (Pi)/(2) and sin theta = 1/2 then the value of sin emptyset is____

    Prove that 4 sin theta sin(pi/3 + theta) sin (pi/3-theta) = sin 3 theta

    If 0 lt theta lt pi/2 and sin 2 theta = cos 3 theta, then the value of sin theta is-

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