Solution 4.3:8d

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It seems natural to try to use the addition formula on the numerator of the left-hand side:
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It seems natural to try to use the addition formula on the numerator of the left-hand side,
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{{Displayed math||<math>\begin{align}
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<math>\begin{align}
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\frac{\cos (u+v)}{\cos u\cos v}
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& \frac{\cos \left( u+v \right)}{\cos u\cos v}=\frac{\cos u\centerdot \cos v-\sin u\centerdot \sin v}{\cos u\centerdot \cos v} \\
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&= \frac{\cos u\cdot\cos v - \sin u\cdot\sin v}{\cos u\cdot\cos v}\\[5pt]
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& =1-\frac{\sin u\centerdot \sin v}{\cos u\centerdot \cos v}=1-\tan u\centerdot \tan v. \\
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&= 1-\frac{\sin u\cdot\sin v}{\cos u\cdot\cos v}\\[5pt]
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\end{align}</math>
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&= 1-\tan u\cdot\tan v\,\textrm{.}
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\end{align}</math>}}

Current revision

It seems natural to try to use the addition formula on the numerator of the left-hand side,

\displaystyle \begin{align}

\frac{\cos (u+v)}{\cos u\cos v} &= \frac{\cos u\cdot\cos v - \sin u\cdot\sin v}{\cos u\cdot\cos v}\\[5pt] &= 1-\frac{\sin u\cdot\sin v}{\cos u\cdot\cos v}\\[5pt] &= 1-\tan u\cdot\tan v\,\textrm{.} \end{align}

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