What is the value of cos^2((7pi)/8) ?

The value of cos^2((7pi)/8) is (2+sqrt(2))/4

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cos^2((7pi)/8)

cos^{2} (\frac{7 π}{8})

\frac{2 + 2}{4}

Solution steps

cos^{2} (\frac{7 π}{8})

Rewrite using trig identities:

cos (\frac{7 π}{8}) = - cos (\frac{π}{8})

= (- cos (\frac{π}{8}))^{2}

(- cos (\frac{π}{8}))^{2} = cos^{2} (\frac{π}{8})

= cos^{2} (\frac{π}{8})

Rewrite using trig identities:

\frac{1 + cos ( \frac{π}{4} )}{2}

= \frac{1 + cos ( \frac{π}{4} )}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

= \frac{1 + \frac{2}{2}}{2}

Simplify

\frac{1 + \frac{2}{2}}{2} : \frac{2 + 2}{4}

= \frac{2 + 2}{4}

3 + 2 sin (- \frac{π}{6})

\frac{60 sin ( 1 5 ^{\circ} )}{400}

- tan^{2} (0)

e^{2 s i n (\frac{π}{2})}

cos (30.9 6^{\circ})

What is the value of cos^2((7pi)/8) ?
The value of cos^2((7pi)/8) is (2+sqrt(2))/4