simplify cos2θ ÷ sinθ + cosθ
There are lots of ways to massage this, but none really very simple...
cos2θ ÷ sinθ + cosθ
= (cos2θ + sinθ cosθ)/sinθ
= (2cos2θ + sin2θ)/(2sinθ)
Ahh. Maybe you meant
cos2θ ÷ (sinθ + cosθ)
= (cos^2θ - sin^2θ)/(cosθ + sinθ)
= cosθ - sinθ