Question

I'm really having trouble simplifying trigonometric expressions, I understand the identities, but sometimes I get stuck, and really need an explanation

sint + tan t
________
tan t

Answer 1

$\bf \cfrac{sin(t)+tan(t)}{tan(t)}\impliedby \textit{distributing the denominator} \\\\\\ \cfrac{sin(t)}{tan(t)}+\cfrac{tan(t)}{tan(t)}\implies \cfrac{sin(t)}{\frac{sin(t)}{cos(t)}}+1\implies \cfrac{\frac{sin(t)}{1}}{\frac{sin(t)}{cos(t)}}+1 \\\\\\ \cfrac{sin(t)}{1}\cdot \cfrac{cos(t)}{sin(t)}+1\implies cos(t)+1$