Acalculator is broken so that the only keys that still work are the $\sin$, $\cos$, $\tan$, $\cot$, $\arcsin$, $\arccos$, and $\arctan$ buttons. assume that the calculator does real number calculations with infinite precision. all functions are in terms of radians, and you may assume all the values of $x$ below are positive.
(a) find, with proof, a sequence of buttons that will transform $x$ into $\frac{1}{x}$ .
(b) find, with proof, a sequence of buttons that will transform $\sqrt x$ into $\sqrt{x+1}$.
(c) the display initially shows $1$. prove that there is a sequence of buttons that will produce $\frac{3}{\sqrt{5}}$.