Acalculator is broken so that the only keys that still work are the $\sin$, $\cos$, $\tan$, $\cot$, $\sin^{-1}$, $\cos^{-1}$, and $\tan^{-1}$ buttons. assume that the calculator does real number calculations with infinite precision. all functions are in terms of radians.
(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 0. prove that there is a sequence of buttons that will produce $\frac{3}{\sqrt{5}}$.