(сos²(x+π/2)(1/(sin²(x-3π/2)-1)(tg²(x-π/2)+1)))/(ctg²(x+3π/2)+1)=
(sin²x*(1/cos²x-1)*(ctg²x+1))/(tg²x+1)=(sin²x*(tg²x)*(1/sin²x))/(1/cos²x)=
sin²x*(tg²x*ctg²x)=sin²x
(сos²(x+π/2)(1/(sin²(x-3π/2)-1)(tg²(x-π/2)+1)))/(ctg²(x+3π/2)+1)=
(sin²x*(1/cos²x-1)*(ctg²x+1))/(tg²x+1)=(sin²x*(tg²x)*(1/sin²x))/(1/cos²x)=
sin²x*(tg²x*ctg²x)=sin²x