Trigonometry Examples

$\frac{\csc (B)}{\cos (B)} - \frac{\cos (B)}{\sin (B)}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{\frac{1}{\sin (B)}}{\cos (B)} - \frac{\cos (B)}{\sin (B)}$

Step 1.2

Rewrite $\frac{\frac{1}{\sin (B)}}{\cos (B)}$ as a product.

$\frac{1}{\sin (B)} \cdot \frac{1}{\cos (B)} - \frac{\cos (B)}{\sin (B)}$

Step 1.3

Multiply $\frac{1}{\sin (B)}$ by $\frac{1}{\cos (B)}$ .

$\frac{1}{\sin (B) \cos (B)} - \frac{\cos (B)}{\sin (B)}$

Step 2

Simplify each term.

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Step 2.1

Separate fractions.

$\frac{1}{\cos (B)} \cdot \frac{1}{\sin (B)} - \frac{\cos (B)}{\sin (B)}$

Step 2.2

Convert from $\frac{1}{\sin (B)}$ to $\csc (B)$ .

$\frac{1}{\cos (B)} \csc (B) - \frac{\cos (B)}{\sin (B)}$

Step 2.3

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

$\sec (B) \csc (B) - \frac{\cos (B)}{\sin (B)}$

Step 2.4

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

$\sec (B) \csc (B) - \cot (B)$