Simplify csc(theta)^2*sin(theta)

$\csc^{2} (θ) \cdot \sin (θ)$

Step 1

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

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

Step 2

Simplify the expression.

Apply the product rule to $\frac{1}{\sin (θ)}$ .

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

One to any power is one.

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

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

Step 3

Cancel the common factor of $\sin (θ)$ .

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

$\frac{1}{\sin (θ) \sin (θ)} \cdot \sin (θ)$

Cancel the common factor.

$\frac{1}{\sin (θ) \sin (θ)} \cdot \sin (θ)$

Rewrite the expression.

$\frac{1}{\sin (θ)}$

$\frac{1}{\sin (θ)}$

Step 4

Convert from $\frac{1}{\sin (θ)}$ to $\csc (θ)$ .

$\csc (θ)$

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