Question

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

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

Answer 1

The correct option is B $\frac{19\pi }{24}$

$tan(A-B)=1$ $sec(A+B)=\frac{2}{\sqrt{3}}$

$A-B=\frac{\pi }{4}$

$A+B=\frac{11\pi }{6}$

$(A-B)+(A+B)=\frac{25\pi }{12}$

$2A=\frac{5\pi }{12}$

$A=\frac{25\pi }{24}$

$\therefore B=\frac{19\pi }{24}$