Question

Under root of 2 + under root of 2 (1+cos4theata

Answer 1

Answer:

$2cos \alpha$

Step-by-step explanation:

$= \sqrt{2 + \sqrt{2(1 + cos4 \alpha ) } } \\ = \sqrt{2 + \sqrt{2(1 + 2 {cos}^{2} 2 \alpha - 1)} } \\ = \sqrt{2 + \sqrt{4 {cos}^{2}2 \alpha } } \\ = \sqrt{2 + 2cos2 \alpha } \\ = \sqrt{2(1 + cos2 \alpha )} \\ = \sqrt{2(1 + 2 {cos}^{2} \alpha - 1) } \\ = \sqrt{4 {cos}^{2} \alpha } \\ = 2cos \alpha$

Hope it will help you.