Sin²α (1+sin^-1α+ctgα) (1-sin^-1α+ctgα) упростите

Sin²α· (1+1/sinα+ctgα) (1-1/sinα+ctgα)=Sin²α· (1+ctgα+1/sinα) (1+ctgα-1/sin²α)=Sin²α·[ (1+ctgα) ²-1/sin²α]=Sin²α·[ (1+ctgα) ²·sin²α — 1]/sin²α=(1+ctgα) ²/ (1+ctg²α) — 1=(1+ctg²α+2ctgα) / (1+ctg²α) — 1=1+2ctgα/ (1+ctg²α) -1=2ctgα/ (1+ctg²α)=2ctgα/ (1+ctg²α)=2ctgα·sin²α=2cosα·sin²α /sinα=2cosα·sinα=sin2α