If tan(A−B)=1 and sec(A+B)=2/3 then the smallest positive values of ,A and B, respectively, are
25π24,19π24
19π24,25π24
31π24,13π24
13π24,31π24
tan(A−B)=1⇒ A−B=n1π+π4 or A−B=π4,3π4,−3π4,… sec(A+B)=23⇒ A+B=2n2π±π6 or A+B=π6,11π6,…
For the least positive values of ,A and B, we have
A+B=11π6, A−B=π4⇒ B=19π24, A=25π24