Question

$prove that2 \sin \frac{pi}{8} = \sqrt{2 - \sqrt{2} }$
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Answer 1

Step-by-step explanation:

We have,

$2 \sin( \frac{\pi}{8} ) = 2 \sin( \frac{1}{2} \times \frac{\pi}{4} ) = 2 \times \sqrt{ \frac{1 - \cos( \frac{\pi}{4} ) }{2} }$

$= 2 \sqrt{ \frac{ \sqrt{2} - 1 }{2 \sqrt{2} } }$

$= 2 \sqrt{ \frac{2 - \sqrt{2} }{4} }$

$= 2 \times \frac{ \sqrt{2 - \sqrt{2} } }{2}$

$= \sqrt{2 - \sqrt{2} }$