Trigonometry Examples

$\frac{\sin^{2} (x)}{\tan^{2} (x)}$

Step 1

Rewrite $\frac{\sin^{2} (x)}{\tan^{2} (x)}$ as ${(\frac{\sin (x)}{\tan (x)})}^{2}$ .

${(\frac{\sin (x)}{\tan (x)})}^{2}$

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\cos^{2} (x)$