Answer:
A
Step-by-step explanation:
We are given:
[tex]\displaystyle \frac{\sin^2(x)-\sin(x)-2}{\sin(x)-2}[/tex]
To make it simpler and more clear, we can let u = sin(x). So:
[tex]\displaystyle \frac{u^2-u-2}{u-2}[/tex]
Now, it becomes obvious that we can factor, which produces:
[tex]\displaystyle =\frac{(u-2)(u+1)}{u-2}[/tex]
Cancel:
[tex]=u+1[/tex]
And substituting back:
[tex]=\sin(x)+1[/tex]
Hence, our answer is A.
