Question

Show that Cos(22.5) = 1/2.root(2+root(2))

Answer 1

\[\cos 22.5 = \frac{ 1 }{ 2 }\sqrt{2+\sqrt{2}}\]

Answer 2

22.5=45/2 ... so i'd probably say use half angle formula for cos :\[\cos^2\theta=\frac{1+\cos 2 \theta }{2}\]

Answer 3

Walk me through the steps?

Answer 4

\[\cos(45)=\cos(22.5+22.5)=\cos^{2}(22.5)-\sin^{2}(22.5)......but...\sin^{2}(22.5)=1-\cos^{2}(22.5)\]\[\cos(45)=2\cos^{2}(22.5)-1\]\[\frac{ \cos(45)+1 }{ 2 }=\cos^{2}(22.5)\]\[\cos(22.5)=\sqrt{\frac{ \cos(45) +1}{ 2}}\]then you do it