Question

If $\sin (A+B)=\frac{\sqrt{3}}{2}$ and $\cot (A-B)=1$, then find $A$

• A. $27\frac{1^{\circ }}{2}$
• B. $35\frac{1^{\circ }}{2}$
• C. $52\frac{1^{\circ }}{2}$
• D. $55\frac{1^{\circ }}{2}$

Answer 1

Answer: (C)

$52\frac{1^{\circ }}{2}$

Given, $\sin (A+B)=\frac{\sqrt{3}}{2}$
$\Rightarrow A+B={60}^o$ -(1)
And $\cot (A-B)=1$
$\Rightarrow A-B={45}^o$---- (2)
On ddding equations (1) and (2), we get
$\Rightarrow 2A={105}^0$
$\Rightarrow A=52{\frac{1}{2}}^0$