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

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

Step 1

Move $\cos^{2} (θ)$ .

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

Step 2

Apply pythagorean identity.

$1 + \sin (θ) \csc (θ)$

Step 3

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

Reorder $\sin (θ)$ and $\csc (θ)$ .

$1 + \csc (θ) \sin (θ)$

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

$1 + \frac{1}{\sin (θ)} \sin (θ)$

Cancel the common factors.

$1 + 1$

Step 4

Add $1$ and $1$ .

$2$