Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite $\frac{\cos^{2} (x)}{\cot^{2} (x)}$ as ${(\frac{\cos (x)}{\cot (x)})}^{2}$ .

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

Step 1.2

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

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

Step 1.3

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (x)}{\sin (x)}$ .

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

Step 1.4

Write $\cos (x)$ as a fraction with denominator $1$ .

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

Step 1.5

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

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Step 1.5.1

Cancel the common factor.

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

Step 1.5.2

Rewrite the expression.

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

Step 2

Apply pythagorean identity.

$\cos^{2} (x)$