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

`(cos(a-b))/(cos(a)cos(b)) = (cos(a)cos(b)+sin(a)sin(b))/(cos(a)cos(b)) = 1+ (sin(a)sin(b))/(cos(a)cos(b)) =1+tan(a)tan(b)`

Note that I used these identities :
`cos(a-b)=cos(a)cos(b)+sin(a)sin(b)` and
`tan(a)= (sin(a))/(cos(a))`

Answer 2

i belive the answer to be b