Question

If tan(A+B) =$\sqrt{3}$ and sin(A-B) = $\frac{1}{2}$ Where A and B are acute angles.

Then, Cos2A + Sin2B =__

Answer 1

Tan (A+B)=$\sqrt{3}$

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

So, A+B =${60}^{\circ }$………………………………………………….(eq. 1)

and, sin(A-B)=$\frac{1}{2}$

We know that sin ${30}^{\circ }$=$\frac{1}{2}$

So, A-B=${30}^{\circ }$……………………………………………………(eq. 2)

Adding eq.1 and eq.2, we get

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

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