Simplify (3-3cos(theta)^2)/(sin(theta))

$\frac{3 - 3 \cos^{2} (θ)}{\sin (θ)}$

Step 1

Simplify with factoring out.

Factor $3$ out of $3$ .

$\frac{3 (1) - 3 \cos^{2} (θ)}{\sin (θ)}$

Factor $3$ out of $- 3 \cos^{2} (θ)$ .

$\frac{3 (1) + 3 (- \cos^{2} (θ))}{\sin (θ)}$

Factor $3$ out of $3 (1) + 3 (- \cos^{2} (θ))$ .

$\frac{3 (1 - \cos^{2} (θ))}{\sin (θ)}$

Step 2

Apply pythagorean identity.

$\frac{3 \sin^{2} (θ)}{\sin (θ)}$

Step 3

Cancel the common factor of $\sin^{2} (θ)$ and $\sin (θ)$ .

Factor $\sin (θ)$ out of $3 \sin^{2} (θ)$ .

$\frac{\sin (θ) (3 \sin (θ))}{\sin (θ)}$

Cancel the common factors.

Multiply by $1$ .

$\frac{\sin (θ) (3 \sin (θ))}{\sin (θ) \cdot 1}$

Cancel the common factor.

$\frac{\sin (θ) (3 \sin (θ))}{\sin (θ) \cdot 1}$

Rewrite the expression.

$\frac{3 \sin (θ)}{1}$

Divide $3 \sin (θ)$ by $1$ .

$3 \sin (θ)$