Trigonometry Examples

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

Step 1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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

Step 2

Convert from $\frac{\cos^{2} (x)}{\sin^{2} (x)}$ to $\cot^{2} (x)$ .

$\cot^{2} (x) + 1$

Step 3

Rearrange terms.

$1 + \cot^{2} (x)$

Step 4

Apply pythagorean identity.

$\csc^{2} (x)$