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

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

Simplify with factoring out.

Factor $3$ out of $3$ .

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

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

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

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

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

Apply pythagorean identity.

$\frac{3 \sin^{2} (x)}{\sin (x)}$

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

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 \sin (x)}{1}$

Divide $3 \sin (x)$ by $1$ .

$3 \sin (x)$