Trigonometry Examples

$\tan (s) (\cot (s) + \csc (s))$

Step 1

Apply the distributive property.

$\tan (s) \cot (s) + \tan (s) \csc (s)$

Step 2

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

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Step 2.1

Reorder $\tan (s)$ and $\cot (s)$ .

$\cot (s) \tan (s) + \tan (s) \csc (s)$

Step 2.2

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

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

Step 2.3

Cancel the common factors.

$1 + \tan (s) \csc (s)$

Step 3

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

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Step 3.1

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

$1 + \frac{\sin (s)}{\cos (s)} \cdot \frac{1}{\sin (s)}$

Step 3.2

Cancel the common factors.

$1 + \frac{1}{\cos (s)}$

Step 4

Convert from $\frac{1}{\cos (s)}$ to $\sec (s)$ .

$1 + \sec (s)$