Question

50 POINTS WILL VOTTEEE!!!!!!!!!!!!

Which of the following shows the simplified function of sine squared x over the quantity 1 minus cosine x end quantity question mark

1 + cos x
1 − cos x
1 + sin x
1 − sin x

Answer 1

Given:

`\frac{\text{sin}^2x}{1+\text{cos}x}`

To determine the simplified function of the above given, we first use the Pythagorean identity:

`\text{cos}^2(x)+\text{sin}^2(x)=1`

Hence,

`\text{sin}^2x=1-\text{cos}^2x`

We plug in what we know:

`\frac{\text{sn}^2x}{1+\text{cos}x} =\frac{1-\text{cos}^2x}{1+\text{cos}x}`

`\text{Simplify and rearrange}`

`=\frac{-(\text{cos}^2x-1)}{1+\text{cos}x}`

`=\frac{-(\text{cos}x+1)(\text{cos}x-1)}{1+\text{cos}x}`

`=-(\text{cos}x-1)`

`=-\text{cos}x+1`

`=1-\text{cos}x`

Therefore, the answer is:

`1-\text{cos} \ x`