What is the value of csc(18) ?

The value of csc(18) is (sqrt(2)(3+sqrt(5))sqrt(3-\sqrt{5)})/2

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csc(18)

csc (1 8^{\circ})

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

Solution steps

csc (1 8^{\circ})

Rewrite using trig identities:

\frac{1}{sin ( 1 8 ^{\circ} )}

= \frac{1}{sin ( 1 8 ^{\circ} )}

Rewrite using trig identities:

sin (1 8^{\circ}) = \frac{2 3 - 5}{4}

= \frac{1}{\frac{2 3 - 5}{4}}

Simplify

\frac{1}{\frac{2 3 - 5}{4}} : \frac{2 ( 3 + 5 ) 3 - 5}{2}

= \frac{2 ( 3 + 5 ) 3 - 5}{2}

cos (58 5^{\circ})

sin (arcsin (\frac{2}{3}) + arccos (\frac{1}{3}))

- cos (\frac{5 π}{4})

cos (\frac{8 π}{5})

sin (\frac{1}{5})

What is the value of csc(18) ?
The value of csc(18) is (sqrt(2)(3+sqrt(5))sqrt(3-\sqrt{5)})/2