★ Formula Applied :
![\begin{gathered}\sf \bullet\ \; cos^2x-sin^2x=cos2x\\\\\to\ \sf \pink{sin^2x-cos^2x=-cos2x}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5Cbullet%5C%20%5C%3B%20cos%5E2x-sin%5E2x%3Dcos2x%5C%5C%5C%5C%5Cto%5C%20%5Csf%20%5Cpink%7Bsin%5E2x-cos%5E2x%3D-cos2x%7D%5Cend%7Bgathered%7D)
![\begin{gathered}\bullet\ \; \sf sin2x=2.sinx.cosx\\\\\to \sf \blue{sinx.cosx=\dfrac{sin2x}{2}}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cbullet%5C%20%5C%3B%20%5Csf%20sin2x%3D2.sinx.cosx%5C%5C%5C%5C%5Cto%20%5Csf%20%5Cblue%7Bsinx.cosx%3D%5Cdfrac%7Bsin2x%7D%7B2%7D%7D%5Cend%7Bgathered%7D)
![\displaystyle \bullet\ \; \sf \int \dfrac{dx}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbullet%5C%20%5C%3B%20%5Csf%20%5Cint%20%5Cdfrac%7Bdx%7D%7Bx%7D)
![\bullet\ \; \sf \ln (ab)=\ln a+\ln](https://tex.z-dn.net/?f=%5Cbullet%5C%20%5C%3B%20%5Csf%20%5Cln%20%28ab%29%3D%5Cln%20a%2B%5Cln)
★ Explanation :
![\begin{gathered}\displaystyle \sf \int \dfrac{sin^2x-cos^2x}{sinx.cosx}dx\\\\\to \sf \int \dfrac{-cos2x}{\frac{sin2x}{2}}dx\\\\\to \sf \int \dfrac{-2cos2x}{sin2x}dx\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cdisplaystyle%20%5Csf%20%5Cint%20%5Cdfrac%7Bsin%5E2x-cos%5E2x%7D%7Bsinx.cosx%7Ddx%5C%5C%5C%5C%5Cto%20%5Csf%20%5Cint%20%5Cdfrac%7B-cos2x%7D%7B%5Cfrac%7Bsin2x%7D%7B2%7D%7Ddx%5C%5C%5C%5C%5Cto%20%5Csf%20%5Cint%20%5Cdfrac%7B-2cos2x%7D%7Bsin2x%7Ddx%5Cend%7Bgathered%7D)
Lets use substitution method ,
Let , u = sin2x
⇒ du = 2.cos2x.dx
![\begin{gathered}\to \displaystyle \sf \int \dfrac{-du}{u}\\\\\to \sf -\int \dfrac{du}{u}\\\\\to \sf -ln|u|\\\\\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cto%20%5Cdisplaystyle%20%5Csf%20%5Cint%20%5Cdfrac%7B-du%7D%7Bu%7D%5C%5C%5C%5C%5Cto%20%5Csf%20-%5Cint%20%5Cdfrac%7Bdu%7D%7Bu%7D%5C%5C%5C%5C%5Cto%20%5Csf%20-ln%7Cu%7C%5C%5C%5C%5C%5Cend%7Bgathered%7D)
![\to \sf \red{-ln|sin2x|+c}](https://tex.z-dn.net/?f=%5Cto%20%5Csf%20%5Cred%7B-ln%7Csin2x%7C%2Bc%7D)
![\to \sf - \ln |2sinx.cosx|+c](https://tex.z-dn.net/?f=%5Cto%20%5Csf%20-%20%5Cln%20%7C2sinx.cosx%7C%2Bc)
![\to \sf - \ln |sinx.cosx|+(\ln 2+c)](https://tex.z-dn.net/?f=%5Cto%20%5Csf%20-%20%5Cln%20%7Csinx.cosx%7C%2B%28%5Cln%202%2Bc%29)
![\leadsto - \sf \red{\ln |sinx.cosx|+c}\ \; \bigstar](https://tex.z-dn.net/?f=%5Cleadsto%20-%20%5Csf%20%5Cred%7B%5Cln%20%7Csinx.cosx%7C%2Bc%7D%5C%20%5C%3B%20%5Cbigstar)
★ Alternate Method :
![\displaystyle \sf \int \dfrac{sin^2x-cos^2x}{sinx.cosx}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csf%20%5Cint%20%5Cdfrac%7Bsin%5E2x-cos%5E2x%7D%7Bsinx.cosx%7D)
![\displaystyle \to \sf \int \left( \dfrac{sin^2x}{sinx.cosx}-\dfrac{cos^2x}{sinx.cosx}\right)dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cto%20%5Csf%20%5Cint%20%5Cleft%28%20%5Cdfrac%7Bsin%5E2x%7D%7Bsinx.cosx%7D-%5Cdfrac%7Bcos%5E2x%7D%7Bsinx.cosx%7D%5Cright%29dx)
![\begin{gathered}\displaystyle \to \sf \int \left( \dfrac{sinx}{cosx} -\dfrac{cosx}{sinx} \right)dx\\\\\to\ \sf \int (tanx-cotx)dx\\\\\to \sf \int tanx.dx-\int cotx.dx\\\\\to \sf ln|secx|-ln|sinx|+c\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cdisplaystyle%20%5Cto%20%5Csf%20%5Cint%20%5Cleft%28%20%5Cdfrac%7Bsinx%7D%7Bcosx%7D%20-%5Cdfrac%7Bcosx%7D%7Bsinx%7D%20%5Cright%29dx%5C%5C%5C%5C%5Cto%5C%20%5Csf%20%5Cint%20%28tanx-cotx%29dx%5C%5C%5C%5C%5Cto%20%5Csf%20%5Cint%20tanx.dx-%5Cint%20cotx.dx%5C%5C%5C%5C%5Cto%20%5Csf%20ln%7Csecx%7C-ln%7Csinx%7C%2Bc%5Cend%7Bgathered%7D)
![\to \sf ln\left| \dfrac{secx}{sinx}\right|+c](https://tex.z-dn.net/?f=%5Cto%20%5Csf%20ln%5Cleft%7C%20%5Cdfrac%7Bsecx%7D%7Bsinx%7D%5Cright%7C%2Bc)
]
![\leadsto \sf \pink{-ln|sinx.cosx|+c}\ \; \bigstar](https://tex.z-dn.net/?f=%5Cleadsto%20%5Csf%20%5Cpink%7B-ln%7Csinx.cosx%7C%2Bc%7D%5C%20%5C%3B%20%5Cbigstar)
Answer:
1) Saying weird/rude things: Try your best to ignore the child/teen/tween bullying you.
2) Hits you: Get adult involved.
3) Non-Stop Bully: Get parent involved, if parent dosent listen tell friends.
4) Threats to fight you: Go to the counselor.
I'd go with the first option, because if you are writing a first-person you are using the word I a lot. and that gets kind of boring.
The idea that best summarizes this excerpt is that despite differences, America is still a United country.
<h3>What is this excerpt about?</h3>
The excerpt describes the clash between different cultures. This can be seen in fragments such as "one part seems to be always on the verge of fisticuffs with another, blacks and whites, gays and straights, left and right..."
Moreover, in the excerpt the author clarifies in another countries this sitaution led to divisions but this has not happened in America.
<h3>What phrase summarizes the main idea?</h3>
Based on the above, it can be concluded America is a united country even with all the cultural differences.
Learn more about America in: brainly.com/question/9187668
#SPJ1