Trigonometry Examples

$\frac{\csc (b) \tan (b)}{\sec (b)}$

Step 1

Separate fractions.

$\frac{\tan (b)}{1} \cdot \frac{\csc (b)}{\sec (b)}$

Step 2

Rewrite $\sec (b)$ in terms of sines and cosines.

$\frac{\tan (b)}{1} \cdot \frac{\csc (b)}{\frac{1}{\cos (b)}}$

Step 3

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

$\frac{\tan (b)}{1} \cdot \frac{\frac{1}{\sin (b)}}{\frac{1}{\cos (b)}}$

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (b)}$ .

$\frac{\tan (b)}{1} \cdot \frac{\cos (b)}{\sin (b)}$

Step 5

Convert from $\frac{\cos (b)}{\sin (b)}$ to $\cot (b)$ .

$\frac{\tan (b)}{1} \cot (b)$

Step 6

Divide $\tan (b)$ by $1$ .

$\tan (b) \cot (b)$

Step 7

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

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Step 7.1

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

$\cot (b) \tan (b)$

Step 7.2

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

$\frac{\cos (b)}{\sin (b)} \cdot \frac{\sin (b)}{\cos (b)}$

Step 7.3

Cancel the common factors.

$1$