Precalculus Examples

$\frac{1 + \cos (x) \tan (x) \csc (x)}{\csc (x)}$

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

Reorder $\cos (x)$ and $\tan (x)$ .

$\frac{1 + \tan (x) \cos (x) \csc (x)}{\csc (x)}$

Step 1.1.2

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

$\frac{1 + \frac{\sin (x)}{\cos (x)} \cos (x) \csc (x)}{\csc (x)}$

Step 1.1.3

Cancel the common factors.

$\frac{1 + \sin (x) \csc (x)}{\csc (x)}$

Step 1.2

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

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Step 1.2.1

Reorder $\sin (x)$ and $\csc (x)$ .

$\frac{1 + \csc (x) \sin (x)}{\csc (x)}$

Step 1.2.2

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

$\frac{1 + \frac{1}{\sin (x)} \sin (x)}{\csc (x)}$

Step 1.2.3

Cancel the common factors.

$\frac{1 + 1}{\csc (x)}$

Step 1.3

Add $1$ and $1$ .

$\frac{2}{\csc (x)}$

Step 2

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

$\frac{2}{\frac{1}{\sin (x)}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$2 \sin (x)$