Trigonometry Examples

$\tan^{2} (x) (\csc^{2} (x) - 1)$

Step 1

Apply pythagorean identity.

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

Step 2

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

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

Step 3

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

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

Step 4

Apply basic rules of exponents.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

Cancel the common factor of $\cos^{2} (x)$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$1$