Trigonometry Examples

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

Step 1

Reorder $\sin^{2} (x) \csc^{2} (x)$ and $- \sin^{2} (x)$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Rearrange terms.

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

Step 6

Apply pythagorean identity.

$\sin^{2} (x) \cdot \cot^{2} (x)$

Step 7

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

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

Step 8

Apply the product rule to $\frac{\cos (x)}{\sin (x)}$ .

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

Step 9

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

Tap for more steps...

Step 9.1

Cancel the common factor.

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

Step 9.2

Rewrite the expression.

$\cos^{2} (x)$