What is the value of tan^2(27) ?

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

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tan^2(27)

tan^{2} (2 7^{\circ})

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

Solution steps

tan^{2} (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

arctan (\frac{36}{48})

19500 sin (6 0^{\circ}) cos (11 0^{\circ})

arccos (\frac{27}{5 34})

\frac{10 sin ( 6 0 ^{\circ} )}{9}

\frac{10}{cos ( 4 0 ^{\circ} )}

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