Simplify the expression

Question

(sin^2(t)-2sin(t)+1)/(sin(t)-1)

Answer 1

( a - b ) ^ 2 = a ^ 2 - 2 a * b + b ^ 2

[ sin ( t ) - 1 ] ^ 2 =

sin ^ 2 ( t ) - 2 * sin ( t ) * 1 + 1 ^ 2 =

sin ^ 2 ( t ) - 2 sin ( t ) + 1

so :

sin ^ 2 ( t ) - 2 sin ( t ) + 1 = [ sin ( t ) - 1 ] ^ 2

[ sin ^ 2 ( t ) - 2 sin ( t ) + 1 ] / [ sin ( t ) - 1 ] =

[ sin ( t ) - 1 ] ^ 2 / [ sin ( t ) - 1 ] =

sin ( t ) - 1

[ sin ^ 2 ( t ) - 2 sin ( t ) + 1 ] / [ sin ( t ) - 1 ] = sin ( t ) - 1

Answer 2

I don't understand why you squared (sin(t)-1)