What is the value of sec(54) ?

The value of sec(54) is (sqrt(2)(5+sqrt(5))sqrt(5-\sqrt{5)})/(10)

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sec(54)

sec (5 4^{\circ})

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

Solution steps

sec (5 4^{\circ})

Rewrite using trig identities:

\frac{1}{cos ( 5 4 ^{\circ} )}

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

Rewrite using trig identities:

cos (5 4^{\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}

sin (3 \frac{π}{4})

cos (\frac{- 11 π}{12})

tan (\frac{25 π}{12})

arccos (\frac{27}{33})

sin (\frac{1}{2} arccos (\frac{4}{5}))

What is the value of sec(54) ?
The value of sec(54) is (sqrt(2)(5+sqrt(5))sqrt(5-\sqrt{5)})/(10)