Trigonometry Examples

$\frac{\cos (a - b)}{\cos (a) \cos (b)}$

Step 1

Separate fractions.

$\frac{1}{\cos (b)} \cdot \frac{\cos (a - b)}{\cos (a)}$

Step 2

Rewrite $\frac{\cos (a - b)}{\cos (a)}$ as a product.

$\frac{1}{\cos (b)} (\cos (a - b) \frac{1}{\cos (a)})$

Step 3

Write $\cos (a - b)$ as a fraction with denominator $1$ .

$\frac{1}{\cos (b)} (\frac{\cos (a - b)}{1} \cdot \frac{1}{\cos (a)})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Divide $\cos (a - b)$ by $1$ .

$\frac{1}{\cos (b)} (\cos (a - b) \frac{1}{\cos (a)})$

Step 4.2

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

$\frac{1}{\cos (b)} (\cos (a - b) \sec (a))$

Step 5

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

$\sec (b) (\cos (a - b) \sec (a))$

Step 6

Apply the difference of angles identity $\cos (x - y) = \cos (x) \cos (y) + \sin (x) \sin (y)$ .

$\sec (b) ((\cos (a) \cos (b) + \sin (a) \sin (b)) \sec (a))$

Step 7

Simplify by multiplying through.

Tap for more steps...

Step 7.1

Apply the distributive property.

$\sec (b) (\cos (a) \cos (b) \sec (a) + \sin (a) \sin (b) \sec (a))$

Step 7.2

Apply the distributive property.

$\sec (b) \cos (a) \cos (b) \sec (a) + \sec (b) \sin (a) \sin (b) \sec (a)$