Question

If $cosA=\frac{1}{2}$ and $sinB=\frac{1}{\sqrt{2}}$, then the value of $\frac{tanA-tanB}{1+tanAtanB}$ is $2-\sqrt{3}$
If true then enter $1$ and if false then enter $0$

Answer 1

$\cos A=\frac{1}{2}$
$\cos A=\cos 60$
$A={60}^{\circ }$
$\sin B=\frac{1}{\sqrt{2}}$
$\sin B=\sin 45$
$B={45}^{\circ }$
Now, $\frac{tanA-tanB}{1+tanAtanB}$
$\frac{tan60-tan45}{1+tan45tan60}$
$\frac{\sqrt{3}-1}{1+\sqrt{3}}$
$\frac{(\sqrt{3}-1)(\sqrt{3}-1)}{(1+\sqrt{3})(\sqrt{3}-1)}$
$\frac{3+1-2\sqrt{3}}{3-1}$
$2-\sqrt{3}$