What is the value of 5tan(54) ?

The value of 5tan(54) is ((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/4

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5tan(54)

5 tan (5 4^{\circ})

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

Solution steps

5 tan (5 4^{\circ})

Rewrite using trig identities:

tan (5 4^{\circ}) = cot (3 6^{\circ})

= 5 cot (3 6^{\circ})

Rewrite using trig identities:

cot (3 6^{\circ}) = \frac{( 3 10 + 5 2 ) 5 - 5}{20}

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

Simplify

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

= \frac{( 3 10 + 5 2 ) 5 - 5}{4}

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

28 sin (3 0^{\circ})

arcsin (0.866)

2 cos (\frac{2 π}{6})

4 cos (- \frac{π}{3})

What is the value of 5tan(54) ?
The value of 5tan(54) is ((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/4