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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)#