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

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

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csc(pi/8)

csc (\frac{π}{8})

2 2 - 2 + 2 2 - 2

Solution steps

csc (\frac{π}{8})

Rewrite using trig identities:

\frac{1}{sin ( \frac{π}{8} )}

= \frac{1}{sin ( \frac{π}{8} )}

Rewrite using trig identities:

sin (\frac{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

4 sin (4 5^{\circ})

sin (- 36 0^{\circ})

40 sin (6 0^{\circ})

arcsin (\frac{6}{7})

sin (\frac{20 π}{3})

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