What is the value of cos^2((9pi)/8)-cos(2*(9pi)/8) ?

The value of cos^2((9pi)/8)-cos(2*(9pi)/8) is (2-sqrt(2))/4

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cos^2((9pi)/8)-cos(2*(9pi)/8)

cos^{2} (\frac{9 π}{8}) - cos (2 \cdot \frac{9 π}{8})

\frac{2 - 2}{4}

Solution steps

cos^{2} (\frac{9 π}{8}) - cos (2 \cdot \frac{9 π}{8})

Simplify:

2 \cdot \frac{9 π}{8} = \frac{9 π}{4}

= cos^{2} (\frac{9 π}{8}) - cos (\frac{9 π}{4})

cos (\frac{9 π}{4}) = cos (\frac{π}{4})

= cos^{2} (\frac{9 π}{8}) - cos (\frac{π}{4})

Rewrite using trig identities:

cos^{2} (\frac{9 π}{8}) = \frac{1 + cos ( \frac{π}{4} )}{2}

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

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

sin (- 132 0^{\circ})

3 cos (4)

\frac{cos ^{2} ( π )}{2}

1 - sin (3 3^{\circ})

cos (arctan (\frac{1}{5}))

What is the value of cos^2((9pi)/8)-cos(2*(9pi)/8) ?
The value of cos^2((9pi)/8)-cos(2*(9pi)/8) is (2-sqrt(2))/4