Cosecant of 30 Degrees

Theorem

$\csc 30^\circ = \csc \dfrac \pi 6 = 2$

where $\csc$ denotes cosecant.

Proof

 $\displaystyle \csc 30^\circ$ $=$ $\displaystyle \frac 1 {\sin 30^\circ}$ Cosecant is Reciprocal of Sine $\displaystyle$ $=$ $\displaystyle \frac 1 {\frac 1 2}$ Sine of $30^\circ$ $\displaystyle$ $=$ $\displaystyle 2$ multiplying top and bottom by $2$

$\blacksquare$