Simplify csc(x)-cos(x)^2csc(x)

$\csc (x) - \cos^{2} (x) \csc (x)$

Step 1

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

Multiply by $1$ .

$\csc (x) \cdot 1 - \cos^{2} (x) \csc (x)$

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

$\csc (x) \cdot 1 + \csc (x) (- \cos^{2} (x))$

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

$\csc (x) (1 - \cos^{2} (x))$

Step 2

Apply pythagorean identity.

$\csc (x) \sin^{2} (x)$

Step 3

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

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

Step 4

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

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

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

Cancel the common factor.

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

Rewrite the expression.

$\sin (x)$