Solution 4.3:8d

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 4.3:8d moved to Solution 4.3:8d: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
It seems natural to try to use the addition formula on the numerator of the left-hand side:
-
<center> [[Image:4_3_8d.gif]] </center>
+
 
-
{{NAVCONTENT_STOP}}
+
 
 +
<math>\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}</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}

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_4.3:8d"