What is the value of sec(72) ?

The value of sec(72) is (sqrt(2)(3+sqrt(5))sqrt(3-\sqrt{5)})/2

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sec(72)

sec (7 2^{\circ})

\frac{2 ( 3 + 5 ) 3 - 5}{2}

Solution steps

sec (7 2^{\circ})

Rewrite using trig identities:

\frac{1}{cos ( 7 2 ^{\circ} )}

= \frac{1}{cos ( 7 2 ^{\circ} )}

Rewrite using trig identities:

cos (7 2^{\circ}) = \frac{2 3 - 5}{4}

= \frac{1}{\frac{2 3 - 5}{4}}

Simplify

\frac{1}{\frac{2 3 - 5}{4}} : \frac{2 ( 3 + 5 ) 3 - 5}{2}

= \frac{2 ( 3 + 5 ) 3 - 5}{2}

arccos (cos (\frac{π}{6}))

\frac{2 cos ^{2} ( 4 5 ^{\circ} ) + 3 csc ( 3 7 ^{\circ} )}{2 tan ( 4 5 ^{\circ} )}

sin (2 arcsin (1))

sec (\frac{17 π}{4})

cos (arctan (\frac{5}{12}))

What is the value of sec(72) ?
The value of sec(72) is (sqrt(2)(3+sqrt(5))sqrt(3-\sqrt{5)})/2