Solution 4.3:8d
From Förberedande kurs i matematik 1
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| - | {{ | + | It seems natural to try to use the addition formula on the numerator of the left-hand side, |
| - | + | ||
| - | {{ | + | {{Displayed math||<math>\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}</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} |
