Question

If $\sin (A+B)=\frac{\sqrt{3}}{2}$ and $\cot (A-B)=\sqrt{3}$ then find the value of $B$.

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${10}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is A ${15}^{\circ }$

Given, $\sin (A+B)=\frac{\sqrt{3}}{2}$
$\Rightarrow A+B={60}^o$ -(1)
And $\cot (A-B)=\sqrt{3}$
$\Rightarrow A-B={30}^o$---- (2)
Subtracting eqn 2 from 1
$\Rightarrow 2B={30}^0$
$\Rightarrow B={15}^0$