please solve this Establish the identity cosalpha betacosal

Establish the identity cos(alpha + beta)/cos(alpha - beta)=1 - tan alpha tan beta/1+ tan alpha tan beta

Solution

cos(a+b) = cosacosb-sinasinb
cos(a-b) = cosacosb+sinasinb

cos(a+b)/cos(a-b) = cosacosb-sinasinb/[cosacosb+sinasinb]
=(1-sinasinb/cosacosb)/(1-sinasinb/cosacosb)
=1-tanatanb/1+tanatanb