Trigonometry Examples

$(\tan (x) + \cot (x)) \tan (x)$

Step 1

Apply the distributive property.

$\tan (x) \tan (x) + \cot (x) \tan (x)$

Step 2

Multiply $\tan (x) \tan (x)$ .

Tap for more steps...

Step 2.1

Raise $\tan (x)$ to the power of $1$ .

$\tan^{1} (x) \tan (x) + \cot (x) \tan (x)$

Step 2.2

Raise $\tan (x)$ to the power of $1$ .

$\tan^{1} (x) \tan^{1} (x) + \cot (x) \tan (x)$

Step 2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\tan (x)}^{1 + 1} + \cot (x) \tan (x)$

Step 2.4

Add $1$ and $1$ .

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

Step 3

Rewrite in terms of sines and cosines, then cancel the common factors.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Cancel the common factors.

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

Step 4

Apply pythagorean identity.

$\sec^{2} (x)$