Question

(sin^2(x)+2sin(x)+1)/(sin(x)+1)

Answer 1

The numerator is a quadratic in sin x.
One way to make it easier to understand is to do a substitution.
Let \(z = \sin x\)
Then \(\sin^2 x = z^2\)

Answer 2

Start by substituting z for \(\sin x\) and \(z^2\) for \(\sin ^2 x\).
What do you get?

Answer 3

\[(z^2+2z+1)/(z+1)\]
=z+1

Answer 4

Correct, so far.
Now you need to substitute back \(\sin x \) for z.