Solution 4.3:8d
From Förberedande kurs i matematik 1
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} |
