What is the value of cot((6pi)/5) ?

The value of cot((6pi)/5) is ((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/(20)

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cot((6pi)/5)

cot (\frac{6 π}{5})

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

Solution steps

cot (\frac{6 π}{5})

cot (\frac{6 π}{5}) = cot (\frac{π}{5})

= cot (\frac{π}{5})

Rewrite using trig identities:

\frac{cos ( \frac{π}{5} )}{sin ( \frac{π}{5} )}

= \frac{cos ( \frac{π}{5} )}{sin ( \frac{π}{5} )}

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

Rewrite using trig identities:

sin (\frac{π}{5}) = \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}

\frac{13}{tan ( 9 0 ^{\circ} )}

\frac{150}{sin ( 1 5 ^{\circ} )}

tan (21 5^{\circ})

6 sin (\frac{5 π}{4})

1 - 2 sin^{2} (4 0^{\circ})

What is the value of cot((6pi)/5) ?
The value of cot((6pi)/5) is ((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/(20)