Wie vereinfacht man $\frac{cos (2 θ)}{cos θ - sin θ}$ $cos (2theta) / (costheta-sintheta)$ ?

$\Rightarrow cos θ + sin θ$ $=> color(green)(cos theta + sin theta)$

$\frac{cos (2 θ)}{cos θ - sin θ}$ $cos (2theta) / (cos theta - sin theta)$

Aus der obigen Tabelle $cos 2 θ = {cos}^{2} θ - {sin}^{2} θ$ $cos 2theta = cos^2 theta - sin^2 theta$

$\Rightarrow \frac{{cos}^{2} θ - {sin}^{2} θ}{cos θ - sin θ}$ $=> (cos^2 theta - sin^2 theta) / (cos theta - sin theta)$

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

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

Wie vereinfacht man cos (2theta) / (costheta-sintheta) cos(2θ)cosθ−sinθcos (2theta) / (costheta-sintheta) ?