What is the value of tan(54) ?

The value of tan(54) is ((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/(20)

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tan(54)

tan (5 4^{\circ})

\frac{( 3 10 + 5 2 ) 5 - 5}{20}

Solution steps

tan (5 4^{\circ})

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

\frac{\frac{5 + 1}{4}}{\frac{2 5 - 5}{4}} : \frac{( 3 10 + 5 2 ) 5 - 5}{20}

= \frac{( 3 10 + 5 2 ) 5 - 5}{20}

cos (157. 5^{\circ})

tan (arccos (- \frac{4}{5}))

sin (\frac{- π}{3})

sin (\frac{- π}{6})

\frac{sin ( π )}{2}

What is the value of tan(54) ?
The value of tan(54) is ((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/(20)