$y = 1 + {\sin ^2}\phi + {\sin ^4}\phi + .... = \frac{1}{{(1 - {{\sin }^2}\phi )}} = \frac{1}{{{{\cos }^2}\phi }}$
$z = 1 + {\cos ^2}\phi {\sin ^2}\phi + {\cos ^4}\phi {\sin ^4}\phi + .. = \frac{1}{{(1 - {{\cos }^2}\phi {{\sin }^2}\phi )}}$
Now $xyz = \frac{1}{{{{\sin }^2}\phi {{\cos }^2}\phi (1 - {{\cos }^2}\phi {{\sin }^2}\phi )}}$
$xy + z = \frac{1}{{{{\sin }^2}\phi {{\cos }^2}\phi }} + \frac{1}{{1 - {{\cos }^2}\phi {{\sin }^2}\phi }}$
$ = \frac{1}{{{{\sin }^2}\phi {{\cos }^2}\phi (1 - {{\cos }^2}\phi {{\sin }^2}\phi )}} = xyz$
which is given in $(b)$
Also $x + y + z = xyz$, which is given in $(c)$.
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