Question

Complete the identity. cos (alpha - beta)/cos alpha cos beta=?

A. 1 + cot α cot β

B. tan α tan β + cot β

C. 1 + tan α tan β

D. 1 + cot α tan β

Answer 1

When you see a formula like this, try to operate, so you will see some identities sooner or later. In this case, we have a substraction identity:

\frac{cos ( \alpha - \beta )}{cos \alpha cos \beta } = \frac{cos \alpha cos \beta + sin \alpha sin \beta }{cos \alpha cos \beta } = 1 + tan α · tan β

Explanation:

Answer 2

When you see a formula like this, try to operate, so you will see some identities sooner or later. In this case, we have a substraction identity:


`(cos ( \alpha - \beta ))/(cos \alpha cos \beta )` =
`(cos \alpha cos \beta + sin \alpha sin \beta )/(cos \alpha cos \beta )` = 1 + tan α · tan β