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If the sum of the roots of the equation `sin^(2)theta=k,(0ltk lt 1)` lying in `[0,2pi]` is equal to the angles of a n-sided regular polygon, then the

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If the sum of the roots of the equation `sin^(2)theta=k,(0ltk lt 1)` lying in `[0,2pi]` is equal to the angles of a n-sided regular polygon, then the value of n is
A. 6
B. 4
C. 2
D. none of these
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Correct Answer - A
`sin^(2)theta = k` gives four roots
`theta, pi-theta pi + theta` and `2pi - theta`
`rArr` the sum of the roots `=4pi=(n-2)pi rArr n = 6`.
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