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

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

Simplify each term.

Rewrite in terms of sines and cosines, then cancel the common factors.

Reorder $\sin (θ)$ and $\csc (θ)$ .

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

Rewrite $\sin (θ) \csc (θ)$ in terms of sines and cosines.

$\sin^{2} (θ) + \frac{1}{\sin (θ)} \sin (θ) \cos^{2} (θ)$

Cancel the common factors.

$\sin^{2} (θ) + 1 \cos^{2} (θ)$

Multiply $\cos^{2} (θ)$ by $1$ .

$\sin^{2} (θ) + \cos^{2} (θ)$

Apply pythagorean identity.

$1$