Wie vereinfacht man # (1 + cos x) (1-cos x) #?

Expand the brackets using FOIL , or the method you use.

#rArr (1 + cosx)(1 - cosx) = 1 -cosx + cosx - cos^2 x #
#= 1 - cos^2 x#

using the identity #color(red)(|bar(ul(color(white)(a/a)color(black)( sin^2 x + cos^2 x = 1 )color(white)(a/a)|)))#

then # 1 - cos^2 x = sin^2 x#