Question

2*sqrt2cos^2(9p/8)-sqrt2

Answer 1

$2 \sqrt{2} cos^2 \frac{9 \pi }{8} -\sqrt{2} = \sqrt{2}(2cos^2 \frac{9 \pi }{8} -1)=\sqrt{2}cos \frac{18 \pi }{8}=\sqrt{2}cos \frac{9 \pi }{4}=\\ \sqrt{2}cos(2 \pi + \frac{ \pi }{4})=\sqrt{2}cos\frac{ \pi }{4}= \sqrt{2} \frac{ \sqrt{2} }{2} =1$