The value of $\sum_\limits {r=0}^{10} \cos ^3 \frac{\pi r}{3}$ is

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

The value of

\sum\limits_{{r=0}}^{10} \cos ^3 \frac{\pi r}{3}

View answer and explanation

Correct option: D

-\frac{1}{8}

Option D (-

\frac{1}{8}

) is correct because by using the trigonometric identity

\cos^3 x = \frac{1}{4}(\cos 3x + 3 \cos x)

and simplifying the summation, the value is found to be -

\frac{1}{8}

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