Question

Prove that cos A / 1 + sin A = tan(450 + A/2)

Answer 1

On RHS, it is probably  tan (45 - A/2) instead of  "tan (45 + A/2)."

$\frac{CosA}{1+SinA}=\frac{Cos^2A/2-Sin^2A/2}{Sin^2A/2+Cos^2A/2+2SinA/2CosA/2}\\\\=\frac{(cosA/2-SinA/2)(CosA/2+SinA/2)}{(CosA/2+SinA/2)^2}\\\\=\frac{1-tanA/2}{1+tanA/2}=\frac{tan45-tanA/2}{1+tan45*tanA/2}\\\\=tan(45-A/2)$