Trigonometry Examples

$\tan (x) \cot (x) - \cos^{2} (x)$

Step 1

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

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Step 1.1

Reorder $\tan (x)$ and $\cot (x)$ .

$\cot (x) \tan (x) - \cos^{2} (x)$

Step 1.2

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

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

Step 1.3

Cancel the common factors.

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

Step 2

Apply pythagorean identity.

$\sin^{2} (x)$