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The possible values of theta in (0, pi) ...

The possible values of `theta in (0, pi)` such that `sin(theta)+sin(4theta)+sin(7theta) = 0` are:

A

`(2pi)/4,pi/4,(4pi)/9,pi/2,(3pi)/4,(8pi)/9`

B

`(pi)/4,(5pi)/12,pi/2,(2pi)/3,(3pi)/4,(8pi)/9`

C

`(2pi)/9,(pi)/4,pi/2,(2pi)/3,(3pi)/4,(35pi)/36`

D

`(2pi)/9,(pi)/4,pi/2,(2pi)/3,(3pi)/4,(8pi)/9`

Text Solution

Verified by Experts

The correct Answer is:
D
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The possible values of theta in (0, pi) such that sin (theta) + sin (4 theta) + sin (7 theta) = 0 are (1) (2 pi) / (9), (i) / (4 ), (4 pi) / (9), (pi) / (2), (3 pi) / (4), (8 pi) / (9) (2) (pi) / (4), (5 pi ) / (12), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (8 pi) / (9) (3) (2 pi) / (9 pi) ), (pi) / (4), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (35 pi) / (36) (4) (2 pi ) / (9), (pi) / (4), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (8 pi) / (9)

sin2theta-sin4theta+sin6theta=0

Knowledge Check

  • The number of values of theta in (0, pi] , such that (cos theta + i sin theta) (cos 3 theta + i sin 3 theta) (cos 5 theta + i sin 5 theta) (cos 7 theta + i sin 7 theta) (cos 9 theta + i sin 9 theta) = -1 is

    A
    11
    B
    13
    C
    14
    D
    16

  • The value of theta in [0, 2 pi] such that the matrix [(2 sin theta - 1, sin theta, cos theta),(sin(theta+pi),2 cos theta - sqrt3, tan theta),(cos(theta-pi),tan (pi-theta),0)] is skew-symmetric is

    A
    `pi/2`
    B
    `pi/4`
    C
    `pi/3`
    D
    `pi/6`

  • The values of theta satisfying sin 7theta = sin 4 theta - sin theta and 0 le theta le pi/2 are

    A
    `pi/9 , pi/4`
    B
    `pi/3, pi/9`
    C
    `pi/6, pi/9`
    D
    `pi/3, pi/4`

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