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·sin²α =
= 2cosα·sin²α /sinα =
= 2cosα·sinα =
= sin2α
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