(tan2 θ) / (tan2 θ + 1) is equivalent to...
a/ cos^2 theta
b/ tan^2 theta
c/ sin^2 theta
d/ 1
e/ none of the above
I hope you mean $\displaystyle \frac{\tan ^2 \theta}{1 + \tan ^2 \theta}$?
$\displaystyle \frac{\tan ^2 \theta}{1 + \tan ^2 \theta} = \dfrac{ \frac{\sin ^2 \theta}{\cos ^2 \theta}}{1 + {\frac{\sin ^2 \theta}{\cos ^2 \theta}}} = \frac{\sin ^2 \theta}{\sin ^ 2 \theta + \cos ^2 \theta} = \sin ^2 \theta$