What is the value of (27)/(tan(72)) ?

The value of (27)/(tan(72)) is (27(5sqrt(2)-sqrt(10))sqrt(5-\sqrt{5)})/(20)

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(27)/(tan(72))

\frac{27}{tan ( 7 2 ^{\circ} )}

\frac{27 ( 5 2 - 10 ) 5 - 5}{20}

Solution steps

\frac{27}{tan ( 7 2 ^{\circ} )}

Rewrite using trig identities:

tan (7 2^{\circ}) = \frac{2 tan ( 3 6 ^{\circ} )}{1 - tan ^{2} ( 3 6 ^{\circ} )}

= \frac{27}{\frac{2 t a n ( 3 6 ^{\circ} )}{1 - t a n ^{2} ( 3 6 ^{\circ} )}}

Simplify

= \frac{27 ( 1 - tan ^{2} ( 3 6 ^{\circ} ) )}{2 tan ( 3 6 ^{\circ} )}

Rewrite using trig identities:

tan (3 6^{\circ}) = \frac{2 ( 5 - 1 ) 5 - 5}{4}

= \frac{27 ( 1 - ( \frac{2 ( 5 - 1 ) 5 - 5}{4} ) ^{2} )}{2 \cdot \frac{2 ( 5 - 1 ) 5 - 5}{4}}

Simplify

\frac{27 ( 1 - ( \frac{2 ( 5 - 1 ) 5 - 5}{4} ) ^{2} )}{2 \cdot \frac{2 ( 5 - 1 ) 5 - 5}{4}} : \frac{27 ( 5 2 - 10 ) 5 - 5}{20}

= \frac{27 ( 5 2 - 10 ) 5 - 5}{20}

cos^{3} (5)

48 cos (6 0^{\circ})

tan (5 0^{\circ}) + tan (2 0^{\circ})

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

sin (138 0^{\circ})

What is the value of (27)/(tan(72)) ?
The value of (27)/(tan(72)) is (27(5sqrt(2)-sqrt(10))sqrt(5-\sqrt{5)})/(20)