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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

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

B

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

C

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

D

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

Text Solution

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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)

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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

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