Question

cos 80 / (cos 40 + sin 40 )

Answer 1

$frac{cos80}{cos40+sin40}=frac{cos^240-sin^240}{cos40+sin40}=frac{(cos40-sin40)(cos40+sin40)}{ccos40+sin40}=\\=cos40-sin40=cos40-sin(90-50)=cos40-cos50=\\=-2sinfrac{40+50}{2}cdot sinfrac{40-50}{2}=-2sin45cdot sin(-5)=-sqrt2sin5$