Answer:
his job that is the answer
Answer:
Information from the story:
- "But his education had not gotten very far when he picked up his own trick that no other seal had learned - how to escape from our little shed."
- "I never again attempted to recapture Nab, nor have I had an opportunity to repay him for towing me to Seal Rocks; but I have seen him a number of times since, and have often heard his happy bark from the rocks along the coast."
Explanation:
<em>These two sentences would help any student form an intending thesis statement for the essay "Saved by a Seal"</em>
★ 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)
Okay let's begin , " Sometimes , not one single fish would make an appearance " Appearance was spelled incorrectly . Then , "As an adolescent, I met a new group of friends." Adolescent was spelled incorrectly . Those were the only two I caught that was misspelled
Okay you too :))))))))))))))))