What is the value of sec(pi/8)-1/((pi/8)^3)+5 ?

The value of sec(pi/8)-1/((pi/8)^3)+5 is 2sqrt(2+\sqrt{2)}-sqrt(2)sqrt(2+\sqrt{2)}-(512)/(pi^3)+5

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sec(pi/8)-1/((pi/8)^3)+5

sec (\frac{π}{8}) - \frac{1}{( \frac{π}{8} ) ^{3}} + 5

2 2 + 2 - 2 2 + 2 - \frac{512}{π ^{3}} + 5

Solution steps

sec (\frac{π}{8}) - \frac{1}{( \frac{π}{8} ) ^{3}} + 5

Rewrite using trig identities:

sec (\frac{π}{8}) = 2 2 + 2 - 2 2 + 2

= 2 2 + 2 - 2 2 + 2 - \frac{1}{( \frac{π}{8} ) ^{3}} + 5

Simplify

2 2 + 2 - 2 2 + 2 - \frac{1}{( \frac{π}{8} ) ^{3}} + 5 : 2 2 + 2 - 2 2 + 2 - \frac{512}{π ^{3}} + 5

= 2 2 + 2 - 2 2 + 2 - \frac{512}{π ^{3}} + 5

\frac{3.7}{cos ( 6 4 ^{\circ} )}

sin (2 (π))

arccos (\frac{4.6}{8.6})

cos (9 4^{\circ}) cos (1 8^{\circ}) + sin (9 4^{\circ}) sin (1 8^{\circ})

arcsin (\frac{8}{15})

What is the value of sec(pi/8)-1/((pi/8)^3)+5 ?
The value of sec(pi/8)-1/((pi/8)^3)+5 is 2sqrt(2+\sqrt{2)}-sqrt(2)sqrt(2+\sqrt{2)}-(512)/(pi^3)+5