Simplify (sin(theta)^2)/(cos(theta)^2+sin(theta)^2)

$\frac{\sin^{2} (θ)}{\cos^{2} (θ) + \sin^{2} (θ)}$

Rearrange terms.

$\frac{\sin^{2} (θ)}{\sin^{2} (θ) + \cos^{2} (θ)}$

Apply pythagorean identity.

$\frac{\sin^{2} (θ)}{1}$

Divide $\sin^{2} (θ)$ by $1$ .

$\sin^{2} (θ)$