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Dvinal [7]
3 years ago
14

Someone read this and just tell me in short words about what is says.

English
1 answer:
jok3333 [9.3K]3 years ago
8 0

Answer:

Explanation:

A person with aphasia may have trouble understanding, speaking, reading, or writing. ... Or you might say a word that does not make much sense, like "radio" for "ball." Switch ... For example, it may be hard to tell time, count money, or add and subtract. ... Ask me to draw, write, or point when I am having trouble talking.

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Xelga [282]

★ Formula Applied :

\begin{gathered}\sf \bullet\ \; cos^2x-sin^2x=cos2x\\\\\to\ \sf \pink{sin^2x-cos^2x=-cos2x}\end{gathered}

\begin{gathered}\bullet\ \; \sf sin2x=2.sinx.cosx\\\\\to \sf \blue{sinx.cosx=\dfrac{sin2x}{2}}\end{gathered}

\displaystyle \bullet\ \; \sf \int \dfrac{dx}{x}

\bullet\ \; \sf \ln (ab)=\ln a+\ln

★ 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}

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}

\to \sf \red{-ln|sin2x|+c}

\to \sf - \ln |2sinx.cosx|+c

\to \sf - \ln |sinx.cosx|+(\ln 2+c)

\leadsto - \sf \red{\ln |sinx.cosx|+c}\ \; \bigstar

★ Alternate Method :

\displaystyle \sf \int \dfrac{sin^2x-cos^2x}{sinx.cosx}

\displaystyle \to \sf \int \left( \dfrac{sin^2x}{sinx.cosx}-\dfrac{cos^2x}{sinx.cosx}\right)dx

\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}

\to \sf ln\left| \dfrac{secx}{sinx}\right|+c

\begin{gathered}\to \sf ln\left| \dfrac{1}{sinx.cosx} \right|+c\\\\\end{gathered}]

\leadsto \sf \pink{-ln|sinx.cosx|+c}\ \; \bigstar

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