The simplified form of the given expression is 2tanx. Option C is correct.
<h2>Trigonometry identity</h2>
Given the following trigonometry identity:
![\frac{cosx}{1-sinx} -\frac{cosx}{1+sinx}](https://tex.z-dn.net/?f=%5Cfrac%7Bcosx%7D%7B1-sinx%7D%20-%5Cfrac%7Bcosx%7D%7B1%2Bsinx%7D%20)
<h3>Simplify the expression</h3>
Find the LCM of the expression to have:
![=\frac{cosx}{1-sinx} -\frac{cosx}{1+sinx} \\ =\frac{cosx(1+sinx)-(cosx(1-sinx)}{(1-sinx)(1+sinx)} \\ =\frac{cosx+cosxsinx-cosx+cosxsinx}{1-sin^2x}\\ =\frac{2cosxsins}{cos^2x } \\ =\frac{2cosxsinx}{cos^2x}\\ ](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bcosx%7D%7B1-sinx%7D%20-%5Cfrac%7Bcosx%7D%7B1%2Bsinx%7D%20%5C%5C%0A%3D%5Cfrac%7Bcosx%281%2Bsinx%29-%28cosx%281-sinx%29%7D%7B%281-sinx%29%281%2Bsinx%29%7D%20%5C%5C%0A%3D%5Cfrac%7Bcosx%2Bcosxsinx-cosx%2Bcosxsinx%7D%7B1-sin%5E2x%7D%5C%5C%0A%20%3D%5Cfrac%7B2cosxsins%7D%7Bcos%5E2x%20%7D%20%5C%5C%0A%3D%5Cfrac%7B2cosxsinx%7D%7Bcos%5E2x%7D%5C%5C%0A%20)
This can be simplified further to have:
![=\frac{2sinxcosx}{cos^2x}\\ =\frac{2sinx}{cosx}\\ =2tanx](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2sinxcosx%7D%7Bcos%5E2x%7D%5C%5C%0A%20%3D%5Cfrac%7B2sinx%7D%7Bcosx%7D%5C%5C%0A%20%3D2tanx)
Therefore the simplified form of the given expression is 2tanx.
Learn more on trigonometry function here: brainly.com/question/4515552
Answer:
if I'm not wrong the answer should be 403,000
Answer:
10.4%
Step-by-step explanation:
percent = part/whole * 100%
percent = $3830.50/$36,825 * 100%
percent = 10.4%
Answer:
1/4
Step-by-step explanation:
Mrs. Lincoln has 15 girls and 10 boys in her homeroom. She randomly selects two students. The total number of students is 25.
The probability of choosing one girl is:
15 / 25 = 3 / 5
Now, 24 students are left.
The probability of choosing one boy is:
10 / 24 = 5 / 12
Therefore, the probability of choosing one girl and one boy is:
3 / 5 * 5 / 12
= 3 / 12
= 1/4