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Leokris [45]
3 years ago
10

Is that ___________ book or mine? Choose the word or phrase that best completes the sentence. A) you'r B) you're C) your D) your

e
English
2 answers:
RSB [31]3 years ago
3 0

the answer is c) your

Alisiya [41]3 years ago
3 0

Good morning!

The correct answer is C- your

Why?

If it has an apostrophe, like option B, you're, it means you are, just shorted. The other options are not proper which makes the answer, C.

Have a nice day!

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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

4 0
3 years ago
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