Question

If tan(A - B)=1, sec (A + B)= $\frac{2}{\sqrt{3}}$, then the smallest positive value of B is

• A. $\frac{25}{24}\pi$
• B. $\frac{11}{24}\pi$
• C. $\frac{13}{24}\pi$
• D. $\frac{19}{24}\pi$

Answer 1

The correct option is D

$\frac{19}{24}\pi$

$tan(A-B)=1\Rightarrow A-B=\frac{\pi }{4}.....\left(i\right)andsec(A+B)=\frac{2}{\sqrt{3}}\Rightarrow A+B=\frac{11\pi }{6}.....\left(ii\right)from\left(i\right)and\left(ii\right),\Rightarrow B=\frac{19\pi }{24}$