[tex] \frac{(1 + \cos(x))(1 - \cos(x) ) - \sin^{2} (x) }{ \sin(x)(1 - \cos(x) ) } [/tex]
[tex] \frac{1 - \cos^{2} (x) - \sin^{2} (x) }{\sin(x)(1 - \cos(x) )} [/tex]
[tex] \frac{0}{\sin(x)(1 - \cos(x) )} [/tex]
[tex]0[/tex]
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[tex] \frac{(1 + \cos(x))(1 - \cos(x) ) - \sin^{2} (x) }{ \sin(x)(1 - \cos(x) ) } [/tex]
[tex] \frac{1 - \cos^{2} (x) - \sin^{2} (x) }{\sin(x)(1 - \cos(x) )} [/tex]
[tex] \frac{0}{\sin(x)(1 - \cos(x) )} [/tex]
[tex]0[/tex]