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 (2)

$A={45}^{\circ }$ and $B={15}^{\circ }$