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

The value of cos((7pi)/8-pi/2) is (sqrt(2-\sqrt{2)})/2

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cos((7pi)/8-pi/2)

cos (\frac{7 π}{8} - \frac{π}{2})

\frac{2 - 2}{2}

Solution steps

cos (\frac{7 π}{8} - \frac{π}{2})

Simplify:

\frac{7 π}{8} - \frac{π}{2} = \frac{3 π}{8}

= cos (\frac{3 π}{8})

Rewrite using trig identities:

\frac{1 + cos ( \frac{3 π}{4} )}{2}

= \frac{1 + cos ( \frac{3 π}{4} )}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

= \frac{1 - \frac{2}{2}}{2}

Simplify

\frac{1 - \frac{2}{2}}{2} : \frac{2 - 2}{2}

= \frac{2 - 2}{2}

\frac{1}{3} (- 8 cos (0) - \frac{tan ^{2} ( 0 )}{2})

30 sin (5 5^{\circ})

arcsin (\frac{3 3}{6})

\frac{arcsin ( \frac{1}{3} ) - arcsin ( - \frac{1}{3} )}{600}

450 sin (7 5^{\circ})

What is the value of cos((7pi)/8-pi/2) ?
The value of cos((7pi)/8-pi/2) is (sqrt(2-\sqrt{2)})/2