What is the value of csc((9pi)/8) ?

The value of csc((9pi)/8) is -2sqrt(2-\sqrt{2)}-sqrt(2)sqrt(2-\sqrt{2)}

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csc((9pi)/8)

csc (\frac{9 π}{8})

- 2 2 - 2 - 2 2 - 2

Solution steps

csc (\frac{9 π}{8})

Rewrite using trig identities:

\frac{1}{sin ( \frac{9 π}{8} )}

= \frac{1}{sin ( \frac{9 π}{8} )}

Rewrite using trig identities:

sin (\frac{9 π}{8}) = - \frac{2 - 2}{2}

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

Simplify

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

= - 2 2 - 2 - 2 2 - 2

tan (\frac{5 π}{6} + \frac{7 π}{4})

2 sec (\frac{π}{3})

tan (2 arccos (\frac{4}{5}))

sec (102 0^{\circ})

- 2 cos (\frac{5 π}{3})

What is the value of csc((9pi)/8) ?
The value of csc((9pi)/8) is -2sqrt(2-\sqrt{2)}-sqrt(2)sqrt(2-\sqrt{2)}