if tan(a- b)=1 and sec(a+b)=2/root 3 . find the smallest positive values of a and b and also their most general values

Hello Student,

a-b=npi+ pi/4
1/cos(a+b)=sec(a+b)=2/root 3
cos(a+b)=root 3/2
a+b=2npi+pi/6
a=2npi+1/2(pi/4+pi/6)
b=2npi+1/2(pi/6-pi/4)
for n=0,
a_{min}=1/2(pi/4+pi/6)
b_{min}=1/2(pi/6-pi/4)

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty