Trigonometry Examples

$\cot^{2} (a) \cos^{2} (a) - \cot^{2} (a)$

Step 1

Simplify with factoring out.

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Step 1.1

Reorder $\cot^{2} (a) \cos^{2} (a)$ and $- \cot^{2} (a)$ .

$- \cot^{2} (a) + \cot^{2} (a) \cos^{2} (a)$

Step 1.2

Factor $- \cot^{2} (a)$ out of $- \cot^{2} (a)$ .

$- \cot^{2} (a) (1) + \cot^{2} (a) \cos^{2} (a)$

Step 1.3

Factor $- \cot^{2} (a)$ out of $\cot^{2} (a) \cos^{2} (a)$ .

$- \cot^{2} (a) (1) - \cot^{2} (a) (- 1 \cos^{2} (a))$

Step 1.4

Factor $- \cot^{2} (a)$ out of $- \cot^{2} (a) (1) - \cot^{2} (a) (- 1 \cos^{2} (a))$ .

$- \cot^{2} (a) (1 - 1 \cos^{2} (a))$

Step 1.5

Rewrite $- 1 \cos^{2} (a)$ as $- \cos^{2} (a)$ .

$- \cot^{2} (a) (1 - \cos^{2} (a))$

Step 2

Apply pythagorean identity.

$- \cot^{2} (a) \sin^{2} (a)$

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

Move the leading negative in $- \frac{\cos^{2} (a)}{\sin^{2} (a)}$ into the numerator.

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$- \cos^{2} (a)$