Lösung 4.3:8d
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
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It seems natural to try to use the addition formula on the numerator of the left-hand side, | It seems natural to try to use the addition formula on the numerator of the left-hand side, | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\begin{align} |
\frac{\cos (u+v)}{\cos u\cos v} | \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] | &= \frac{\cos u\cdot\cos v - \sin u\cdot\sin v}{\cos u\cdot\cos v}\\[5pt] | ||
Version vom 08:57, 22. Okt. 2008
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} |
