Answer
True.
Work Step by Step
Verify the following identity:
$\frac{sin(w)}{sin(w) + cos(w)}=\frac{tan(w)}{1 + tan(w)}$
Multiply numerator and denominator of $\frac{sin(w)}{sin(w) + cos(w)}$ by $sec(w)$:
$\frac{sec(w)sin(w)}{sec(w)(sin(w) + cos(w))} = ^?(tan(w))/(1 + tan(w))$
Since $sec(w)sin(w) = tan(w)$:
$\frac{tan(w)}{sec(w)(cos(w) + sin(w))} = ^?(tan(w))/(1 + tan(w))$
Since $sec(w) (cos(w) + sin(w)) = cos(w) sec(w) + sec(w) sin(w) $
$= \frac{cos(w)}{cos(w)}+ \frac{sin(w)}{cos(w)} = 1 + \frac{sin(w)}{cos(w)} = 1 + tan(w)$:
$\frac{tan(w)}{1 + tan(w)} = ^?\frac{tan(w)}{1 + tan(w)}$
The left hand side and right hand side are identical, thus verifying the identity.
