InterviewSolution
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InterviewSolution
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The value of `sin pi/n + sin (3pi)/n+ sin (5pi)/n+...` to n terms is equal toA. 1B. 0C. `n/2`D. none of these |
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Answer» Correct Answer - B We know that `sin alpha+sin(alpha+beta)+...+sin{alpha+(n-1)beta}` `=(sin{alpha+(n-1)(beta)/(2)}sin((n beta)/(2)))/(sin""(beta)/(2))` `thereforesin""(pi)/(n)+sin""(3pi)/(n)+sin""(5pi)/(n)+....` to n terms `=(sin{(pi)/(n)+(n-1)(pi)/(n)}sin((npi)/(n)))/(sin((pi)/(n)))" "[Here, alpha =(pi)/(n)and beta=(2pi)/(n)]` `=(sinpui sin pi)/(sin""(pi)/(n))=0` |
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