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Solution 4.3:8d

From Förberedande kurs i matematik 1

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m (Lösning 4.3:8d moved to Solution 4.3:8d: Robot: moved page)
Current revision (08:40, 10 October 2008) (edit) (undo)
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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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{{Displayed math||<math>\begin{align}
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\frac{\cos (u+v)}{\cos u\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\cdot\sin v}{\cos u\cdot\cos v}\\[5pt]
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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,

cos(u+v)cosucosv=cosucosvcosucosv−sinusinv=1−sinusinvcosucosv=1−tanutanv.
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