What is the value of tan(27) ?

The value of tan(27) is sqrt(\sqrt{10)sqrt(5-\sqrt{5)}-3sqrt(2)sqrt(5-\sqrt{5)}+11-4sqrt(5)}

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tan(27)

tan (2 7^{\circ})

10 5 - 5 - 32 5 - 5 + 11 - 45

Solution steps

tan (2 7^{\circ})

Rewrite using trig identities:

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

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

Simplify

\frac{1 - \frac{2 5 - 5}{4}}{1 + \frac{2 5 - 5}{4}} : 10 5 - 5 - 32 5 - 5 + 11 - 45

= 10 5 - 5 - 32 5 - 5 + 11 - 45

tan (39 0^{\circ})

tan (2 4^{\circ})

arctan (\frac{2}{- 2})

arccos (sin (\frac{5 π}{3}))

\frac{tan ( 2 0 ^{\circ} ) + tan ( 1 0 ^{\circ} )}{1 - tan ( 2 0 ^{\circ} ) tan ( 1 0 ^{\circ} )}

What is the value of tan(27) ?
The value of tan(27) is sqrt(\sqrt{10)sqrt(5-\sqrt{5)}-3sqrt(2)sqrt(5-\sqrt{5)}+11-4sqrt(5)}