Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

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

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

Step 7

Multiply $\tan (b) \tan (b)$ .

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Step 7.1

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

$\tan^{1} (b) \tan (b)$

Step 7.2

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

$\tan^{1} (b) \tan^{1} (b)$

Step 7.3

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

${\tan (b)}^{1 + 1}$

Step 7.4

Add $1$ and $1$ .

$\tan^{2} (b)$