What is the value of sqrt(1+cos^2(pi/8)) ?

The value of sqrt(1+cos^2(pi/8)) is (sqrt(\sqrt{2)+6})/2

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sqrt(1+cos^2(pi/8))

1 + cos^{2} (\frac{π}{8})

\frac{2 + 6}{2}

Solution steps

1 + cos^{2} (\frac{π}{8})

Rewrite using trig identities:

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

= 1 + \frac{1 + cos ( \frac{π}{4} )}{2}

1 + \frac{1 + cos ( \frac{π}{4} )}{2} = \frac{cos ( \frac{π}{4} ) + 3}{2}

= \frac{cos ( \frac{π}{4} ) + 3}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

= \frac{\frac{2}{2} + 3}{2}

Simplify

\frac{\frac{2}{2} + 3}{2} : \frac{2 + 6}{2}

= \frac{2 + 6}{2}

cot (- \frac{17 π}{3})

6 \cdot 0.5235 sin (48 0^{\circ})

\frac{3}{cos ( 6 5 ^{\circ} )}

cos (0.875)

arctan (\frac{40}{20})

What is the value of sqrt(1+cos^2(pi/8)) ?
The value of sqrt(1+cos^2(pi/8)) is (sqrt(\sqrt{2)+6})/2