Question

If $cosec(A+B)=\frac{2}{\sqrt{3}}$, sec(A-B)=$\frac{2}{\sqrt{3}}$,
$0^{\circ }<A+B\le {90}^{\circ }$,
Find A and B.

• A. 10^o, 50^o
• B. 45^o, 15^o
• C. 30^o, 30^o
• D. 25^o, 35^o

Answer 1

The correct option is B

45^o, 15^o

If A+B lies in this range $0^{\circ }<A+B\le {90}^{\circ }$
$cosec(A+B)=\frac{2}{\sqrt{3}}$ only when $A+B={60}^{\circ }$ ........(1)
sec(A-B)=$\frac{2}{\sqrt{3}}$, only when $A-B={30}^{\circ }$ ........(2)
By Solving equation 1 and equation 2
$A={45}^{\circ }$ and $B={15}^{\circ }$