Question

Please VERIFY (cscx-1)(sinx+1)=cosxcotx

Answer 1

I want to work the left side...

(cscx-1)(sinx+1)=
csc(x)sin(x)+csc(x)-sin(x)-1=
1+csc(x)-sin(x)-1=
csc(x)-sin(x)=

1 / sin(x) - sin(x)=
1 / sin(x) - sin^2(x) / sin(x)=
1 - sin^2(x) / sin(x)=
cos^2(x) / sin(x)=
[ cos(x) / sin(x) ] * cos(x) =
[ cot(x) ] * cos(x) =


both sides are equal.

Answer 2

Wow that makes perfect sense. Thanks!

Answer 3

You welcome !