Trigonometry Examples

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

Step 1

Multiply by $1$ .

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

Step 2

Simplify with factoring out.

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Step 2.1

Factor $\tan^{2} (x)$ out of $- \tan^{2} (x) \sin^{2} (x)$ .

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

Step 2.2

Factor $\tan^{2} (x)$ out of $\tan^{2} (x) \cdot 1 + \tan^{2} (x) (- 1 \sin^{2} (x))$ .

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

Step 2.3

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

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

Step 3

Apply pythagorean identity.

$\tan^{2} (x) \cdot \cos^{2} (x)$

Step 4

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

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

Step 5

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

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\sin^{2} (x)$