Question

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

Answer 1

Answer

Explanation

Given:

$\frac{sin^2x}{1+cosx}$

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

$cos^2(x)+sin^2(x)=1$

Hence,

$sin^2x=1-cos^2x$

We plug in what we know:

$\begin{gathered} \frac{s\imaginaryI n^{2}x}{1+cosx}=\frac{1-cos^2x}{1+cosx} \\ Simplify\text{ and rearrange} \\ =\frac{-(cos^2x-1)}{1+cosx} \\ =\frac{-(cosx+1)(cosx-1)}{1+cosx} \\ =-(cosx-1) \\ =-cosx+1 \\ =1-cosx \end{gathered}$

Therefore, the answer is:

$1-cos\text{ }x$