Wie vereinfacht man cos (2theta) / (costheta-sintheta) ?

Antworten:

=> color(green)(cos theta + sin theta)

Erläuterung:

cos (2theta) / (cos theta - sin theta)

http://www.biology.arizona.edu/biomath/tutorials/Trigonometric/TrigIdentities.html

Aus der obigen Tabelle cos 2theta = cos^2 theta - sin^2 theta

=> (cos^2 theta - sin^2 theta) / (cos theta - sin theta)

=> (cancelcolor(red)(costheta - sin theta) * (cos theta + sin theta)) / cancelcolor(red) (cos theta - sin theta)

=> color(green)(cos theta + sin theta)