[tex]\displaystyle\bf\\\frac{1-Sin\alpha }{Cos\alpha } -\frac{Cos\alpha }{1+Sin\alpha } =\frac{(1-Sin\alpha )\cdot(1+Sin\alpha )-Cos\alpha \cdot Cos\alpha }{Cos\alpha \cdot(1+Sin\alpha )} =\\\\\\=\frac{(1-Sin^{2} \alpha) -Cos^{2}\alpha }{Cos\alpha (1+Sin\alpha )} =\frac{Cos^{2}\alpha -Cos^{2} \alpha }{Cos\alpha (1+Sin\alpha )} =0[/tex]
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[tex]\displaystyle\bf\\\frac{1-Sin\alpha }{Cos\alpha } -\frac{Cos\alpha }{1+Sin\alpha } =\frac{(1-Sin\alpha )\cdot(1+Sin\alpha )-Cos\alpha \cdot Cos\alpha }{Cos\alpha \cdot(1+Sin\alpha )} =\\\\\\=\frac{(1-Sin^{2} \alpha) -Cos^{2}\alpha }{Cos\alpha (1+Sin\alpha )} =\frac{Cos^{2}\alpha -Cos^{2} \alpha }{Cos\alpha (1+Sin\alpha )} =0[/tex]