Fundamentals and Basic Identities

${\displaystyle \csc =\frac{\text{hypotenuse}}{\text{opposite}}}$ and ${\displaystyle \tan =\frac{\text{opposite}}{\text{adjacent}}}$

Therefore ${\displaystyle \csc <!--\; \; -->x\tan <!--\; \; -->x=\frac{\text{hypotenuse}}{\text{opposite}}\ast <!--\; \ast \; -->\frac{\text{opposite}}{\text{adjacent}}}$. Note that the opposite's cancel out, leaving ${\displaystyle \frac{\text{hypotenuse}}{\text{adjacent}}}$. which is the same as secx.