Simplify csc(theta)cot(theta)^2+csc(theta)

$\csc (θ) \cot^{2} (θ) + \csc (θ)$

Reorder $\csc (θ) \cot^{2} (θ)$ and $\csc (θ)$ .

$\csc (θ) + \csc (θ) \cot^{2} (θ)$

Multiply by $1$ .

$\csc (θ) \cdot 1 + \csc (θ) \cot^{2} (θ)$

Simplify with factoring out.

Factor $\csc (θ)$ out of $\csc (θ) \cot^{2} (θ)$ .

$\csc (θ) \cdot 1 + \csc (θ) (\cot^{2} (θ))$

Factor $\csc (θ)$ out of $\csc (θ) \cdot 1 + \csc (θ) (\cot^{2} (θ))$ .

$\csc (θ) \cdot (1 + \cot^{2} (θ))$

Apply pythagorean identity.

$\csc (θ) \cdot \csc^{2} (θ)$

Multiply $\csc (θ)$ by $\csc^{2} (θ)$ by adding the exponents.

Multiply $\csc (θ)$ by $\csc^{2} (θ)$ .

Raise $\csc (θ)$ to the power of $1$ .

$\csc^{1} (θ) \cdot \csc^{2} (θ)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\csc (θ)}^{1 + 2}$

Add $1$ and $2$ .

$\csc^{3} (θ)$