What is the value of sec((5pi)/8) ?

The value of sec((5pi)/8) is -2sqrt(2-\sqrt{2)}-sqrt(2)sqrt(2-\sqrt{2)}

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sec((5pi)/8)

sec (\frac{5 π}{8})

- 2 2 - 2 - 2 2 - 2

Solution steps

sec (\frac{5 π}{8})

Rewrite using trig identities:

\frac{1}{cos ( \frac{5 π}{8} )}

= \frac{1}{cos ( \frac{5 π}{8} )}

Rewrite using trig identities:

cos (\frac{5 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^{2} (3 0^{\circ}) + csc^{2} (6 0^{\circ})

10 \cdot csc (2 3^{\circ})

arcsin (sin (\frac{5 π}{12}))

(cos (\frac{2 π}{3}) + i sin (\frac{2 π}{3}))^{2}

csc (25 5^{\circ})

What is the value of sec((5pi)/8) ?
The value of sec((5pi)/8) is -2sqrt(2-\sqrt{2)}-sqrt(2)sqrt(2-\sqrt{2)}