Question

If $tan(A+B)=\sqrt{3}$ and $tan(A-B)=\frac{1}{\sqrt{3}}$

If $B<A<{90}^{\circ }$, then the value of A and B is

• A. ${45}^{\circ }$ and ${30}^{\circ }$ repectively
• B. ${30}^{\circ }$ and ${15}^{\circ }$ repectively
• C. ${45}^{\circ }$ and ${15}^{\circ }$ repectively
• D. ${60}^{\circ }$ and ${15}^{\circ }$ repectively

Answer 1

The correct option is C ${45}^{\circ }$ and ${15}^{\circ }$ repectively

Given,
$tan(A+B)=\sqrt{3}$

Now, we know that $tan{60}^{\circ }=\sqrt{3}$

$\therefore A+B={60}^{\circ }$ ------------------- (1)

$tan(A-B)=\frac{1}{\sqrt{3}}$

Now, we know that $tan{30}^{\circ }=\frac{1}{\sqrt{3}}$

$\therefore A-B={30}^{\circ }$ --------------------- (2)

Adding equations 1 and 2, we get,

$2A={90}^{\circ }$

$A={45}^{\circ }$

Subtracting 2 from 1, we get,

$2B={30}^{\circ }$

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