Question

If cosec (A+B)=1 and sec(A-B)=2 .find tanA+tanB+1-tanA.tanB

Answer 1

cosec(A+B)=1
cosec(A+B)=cosec90
A+B=90                         ....................(i)
sec(A-B)=2
sec(A-B)=sec60
A-B=60                         .....................(ii)
solving (i) and (ii).
A=75 and B=15
we know the identity that tanA+tanB/1-tanAtanB=tanA+B)
tan(A+B)=tan(75+15)
              =tan90 which is undefined.