If $ω$ is an imaginary cube root of unity, then the value of $c o s {(ω^{17} + ω^{7}) π + \frac{π}{3}}$ is ..............

- \frac{1}{2}

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\frac{1}{2}

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- \frac{\sqrt{3}}{2}

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\frac{\sqrt{3}}{2}

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Solution

The correct option is A $- \frac{1}{2}$
Let $y = c o s {(ω^{17} + ω^{7}) π + \frac{π}{3}}$
$= c o s {({(ω^{3})}^{5} ω^{2} + {(ω^{3})}^{2} ω) π + \frac{π}{3}}$
$\Rightarrow y = c o s {(ω^{2} + ω) π + \frac{π}{3}}$
$= cos (- π + \frac{π}{3})$
$= cos (- \frac{2 π}{3}) = \frac{- 1}{2}$
Ans: A

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