1 - cos-8 - isin-81 - cos-8 - isin-8 8 -

The correct option is B 1 We know that cosθ+isinθ=e^iθ ( 1+cos(π #160; 8 ) isin(π #160; 8 ) 1+cos(π #160; 8 )+isin(π #160; 8 ) ) ^ ...

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Product of Trigonometric Ratios in Terms of Their Sum

1 + cosπ8 - i...

Question

${⎛ ⎜ ⎜ ⎝ \frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} + i sin \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{8} =$

1

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- 1

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2

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\frac{1}{2}

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Solution

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{⎛ ⎜ ⎜ ⎝ \frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} + i sin \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{8}

{(\frac{1 + c o s \frac{π}{8} - i s i n \frac{π}{8}}{1 + c o s \frac{π}{8} + i s i n \frac{π}{8}})}^{8}

{(\frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} - i sin \frac{π}{8}})}^{2} =

{⎛ ⎜ ⎜ ⎝ \begin{matrix} \frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} + i sin \frac{π}{8}} \end{matrix} ⎞ ⎟ ⎟ ⎠}^{8}

{⎛ ⎜ ⎜ ⎝ \frac{c o s \frac{π}{8} - i s i n \frac{π}{8}}{c o s \frac{π}{8} + i s i n \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{4}

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