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Решите задачу:

$\frac{Ctg ^{2}( \frac{ \pi }{2}+ \alpha )*Cos ^{2}( \alpha - \frac{ \pi }{2} ) }{Ctg ^{2}( \alpha - \frac{ \pi }{2}) -Cos ^{2}( \alpha + \frac{ \pi }{2} ) } = \frac{tg ^{2} \alpha *Sin ^{2} \alpha }{tg ^{2} \alpha -Sin ^{2} \alpha }= \frac{ \frac{Sin ^{2} \alpha }{Cos ^{2} \alpha } *Sin ^{2} \alpha }{ \frac{Sin ^{2} \alpha }{Cos ^{2} \alpha }-Sin ^{2} \alpha }=$ $\frac{Sin ^{4} \alpha *Cos ^{2} \alpha }{Cos ^{2} \alpha (Sin ^{2} \alpha -Sin ^{2} \alpha Cos ^{2} \alpha ) } = \frac{Sin ^{4} \alpha }{Sin ^{2} \alpha (1-Cos ^{2} \alpha )} = \frac{Sin ^{4} \alpha }{Sin ^{4} \alpha } =1$