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Allied Angles

The value of ...

Question

The value of $\frac{{(s i n \frac{π}{8} + i c o s \frac{π}{8})}^{8}}{{(s i n \frac{π}{8} - i c o s \frac{π}{8})}^{8}}$ is

A

-1

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B

1

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C

2i

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Solution

The correct option is B 1
$\frac{{(s i n \frac{π}{8} + i c o s \frac{π}{8})}^{8}}{{(s i n \frac{π}{8} - i c o s \frac{π}{8})}^{8}} = {(c o s \frac{π}{8} + i s i n \frac{π}{8})}^{- 16}$
$= c o s 2 π - i s i n 2 π = 1$

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