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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<center> [[Image:4_3_8d.gif]] </center>
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<math>\begin{align}
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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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& =1-\frac{\sin u\centerdot \sin v}{\cos u\centerdot \cos v}=1-\tan u\centerdot \tan v. \\
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\end{align}</math>

Revision as of 11:13, 30 September 2008

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


\displaystyle \begin{align} & \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} \\ & =1-\frac{\sin u\centerdot \sin v}{\cos u\centerdot \cos v}=1-\tan u\centerdot \tan v. \\ \end{align}

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