Final answer to the problem
$1-\sin\left(x\right)$
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Step-by-step Solution
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1
Applying the pythagorean identity: $\cos^2(\theta)=1-\sin(\theta)^2$
$\frac{1-\sin\left(x\right)^2}{1+\sin\left(x\right)}$
Why is 1 - sin(x)^2 = cos(x)^2 ?
2
The difference of the squares of two terms, divided by the sum of the same terms, is equal to the difference of the terms. In other words: $\displaystyle\frac{a^2-b^2}{a+b}=a-b$.
$1-\sin\left(x\right)$
Final answer to the problem
$1-\sin\left(x\right)$