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. ${10}^{\circ },{50}^{\circ }$
• B. ${45}^{\circ },{15}^{\circ }$
• C. ${30}^{\circ },{30}^{\circ }$
• D. ${25}^{\circ },{35}^{\circ }$

Answer 1

The correct option is B

${45}^{\circ },{15}^{\circ }$

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 $B={15}^{\circ }$