Question

помогите, пожалуйста

Answer 1

$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$