Calculus Examples

$\frac{\tan (4 b)}{\tan (5 b)}$

Step 1

Rewrite $\tan (5 b)$ in terms of sines and cosines.

$\frac{\tan (4 b)}{\frac{\sin (5 b)}{\cos (5 b)}}$

Step 2

Rewrite $\tan (4 b)$ in terms of sines and cosines.

$\frac{\frac{\sin (4 b)}{\cos (4 b)}}{\frac{\sin (5 b)}{\cos (5 b)}}$

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (5 b)}{\cos (5 b)}$ .

$\frac{\sin (4 b)}{\cos (4 b)} \cdot \frac{\cos (5 b)}{\sin (5 b)}$

Step 4

Simplify.

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Step 4.1

Convert from $\frac{\sin (4 b)}{\cos (4 b)}$ to $\tan (4 b)$ .

$\tan (4 b) \frac{\cos (5 b)}{\sin (5 b)}$

Step 4.2

Convert from $\frac{\cos (5 b)}{\sin (5 b)}$ to $\cot (5 b)$ .

$\tan (4 b) \cot (5 b)$