Question

Step by step please...​

Answer 1

Answer:

4

Explanation

$\sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2(1 + \frac{1}{ \sqrt{2} }) } } } } } \\ = \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2(1 + \cos( \frac{\pi}{4} ) ) } } } } } \\ = \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2 + 2\sqrt{ \cos {}^{2} ( \frac{\pi}{8} ) } } } } } \\ = = \sqrt{2 + \sqrt{2 + \sqrt{{2 + \sqrt{2(1 + \cos( \frac{\pi}{8}) ) } } } } }$

Repeat the process finally you will get

$2 \cos( \frac{\pi}{ {2}^{7} } ) = 2 \cos( \frac{\pi}{128} )$