If $\displaystyle X = \csc (\arctan(\cos(\text{arccot}(\sec(\arcsin a)))))$

$\displaystyle Y = \sec(\text{arccot}(\sin(\arctan(\csc(\arccos a)))))$;

where $\displaystyle 0\leq a\leq 1$. Find the relation between $\displaystyle X\ $ & $\displaystyle \ Y$. Express them in terms of 'a'.