Trigonometry Examples

$\tan (θ) (\cot (θ) + \tan (θ))$

Step 1

Apply the distributive property.

$\tan (θ) \cot (θ) + \tan (θ) \tan (θ)$

Step 2

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

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Step 2.1

Reorder $\tan (θ)$ and $\cot (θ)$ .

$\cot (θ) \tan (θ) + \tan (θ) \tan (θ)$

Step 2.2

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

$\frac{\cos (θ)}{\sin (θ)} \cdot \frac{\sin (θ)}{\cos (θ)} + \tan (θ) \tan (θ)$

Step 2.3

Cancel the common factors.

$1 + \tan (θ) \tan (θ)$

Step 3

Multiply $\tan (θ) \tan (θ)$ .

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Step 3.1

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

$1 + \tan^{1} (θ) \tan (θ)$

Step 3.2

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

$1 + \tan^{1} (θ) \tan^{1} (θ)$

Step 3.3

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

$1 + {\tan (θ)}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

$1 + \tan^{2} (θ)$

Step 4

Rearrange terms.

$\tan^{2} (θ) + 1$

Step 5

Apply pythagorean identity.

$\sec^{2} (θ)$