What is the value of sec(18) ?

The value of sec(18) is (sqrt(2)(5-sqrt(5))sqrt(5+\sqrt{5)})/(10)

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sec(18)

sec (1 8^{\circ})

\frac{2 ( 5 - 5 ) 5 + 5}{10}

Solution steps

sec (1 8^{\circ})

Rewrite using trig identities:

\frac{1}{cos ( 1 8 ^{\circ} )}

= \frac{1}{cos ( 1 8 ^{\circ} )}

Rewrite using trig identities:

cos (1 8^{\circ}) = \frac{2 5 + 5}{4}

= \frac{1}{\frac{2 5 + 5}{4}}

Simplify

\frac{1}{\frac{2 5 + 5}{4}} : \frac{2 ( 5 - 5 ) 5 + 5}{10}

= \frac{2 ( 5 - 5 ) 5 + 5}{10}

cos (18 0^{\circ}) - sin (18 0^{\circ})

cos (\frac{30}{2})

5 sin (\frac{5 π}{4})

sin (4 (\frac{π}{8}))

- 3.69 sin (0.9 (4))

What is the value of sec(18) ?
The value of sec(18) is (sqrt(2)(5-sqrt(5))sqrt(5+\sqrt{5)})/(10)