How do you find the value of $cos (\frac{π}{8})$ $cos(pi/8)$ ?

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Answer 1 · 2016-06-19T18:49:54

The half angle formula for cosine is $cos x = 2 {cos}^{2} (\frac{x}{2}) - 1$ $cos x= 2 cos^2 (x/2) -1$ .
Thus

cos $\frac{π}{4} = 2 {cos}^{2} (\frac{π}{8}) - 1$ $pi/4 = 2 cos^2 (pi/8) -1$ ,

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

= $\frac{1 + \sqrt{2}}{2 \sqrt{2}}$ $( 1+sqrt2)/(2sqrt2)$ = $\frac{2 + \sqrt{2}}{4}$ $(2+sqrt2)/4$

cos $\frac{π}{8}$ $pi/8$ = $\frac{\sqrt{2 + \sqrt{2}}}{2}$ $sqrt (2+sqrt2) /2$

How do you find the value of cos(π8)cos(pi/8)?