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

i belive the answer to be b

Answer 2

$\frac{cos(a-b)}{cos(a)cos(b)} = \frac{cos(a)cos(b)+sin(a)sin(b)}{cos(a)cos(b)} = 1+ \frac{sin(a)sin(b)}{cos(a)cos(b)} =1+tan(a)tan(b)$

Note that I used these identities :$cos(a-b)=cos(a)cos(b)+sin(a)sin(b)$ and  $tan(a)= \frac{sin(a)}{cos(a)}$