What is the value of tan(72) ?

The value of tan(72) is sqrt(5+2\sqrt{5)}

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tan(72)

tan (7 2^{\circ})

5 + 25

Solution steps

tan (7 2^{\circ})

Rewrite using trig identities:

\frac{sin ( 7 2 ^{\circ} )}{cos ( 7 2 ^{\circ} )}

= \frac{sin ( 7 2 ^{\circ} )}{cos ( 7 2 ^{\circ} )}

Rewrite using trig identities:

sin (7 2^{\circ}) = \frac{2 5 + 5}{4}

Rewrite using trig identities:

cos (7 2^{\circ}) = \frac{2 3 - 5}{4}

= \frac{\frac{2 5 + 5}{4}}{\frac{2 3 - 5}{4}}

Simplify

\frac{\frac{2 5 + 5}{4}}{\frac{2 3 - 5}{4}} : 5 + 25

= 5 + 25

cos (2 3^{\circ})

2 cos (\frac{3 π}{2})

arctan (0.25)

cos (3 3^{\circ})

tan (\frac{9 π}{4})