If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ,

We are given that $5 \theta$ and $4 \theta$ are acute angles satisfying the following condition

$\sin 5 \theta=\cos 4 \theta$. We are asked to find $2 \sin 3 \theta-\sqrt{3} \tan 3 \theta$

$\Rightarrow \sin 5 \theta=\cos 4 \theta$

$\Rightarrow \cos \left(90^{\circ}-5 \theta\right)=\cos 4 \theta$

$\Rightarrow 90^{\circ}-5 \theta=4 \theta$

$\Rightarrow 9 \theta=90^{\circ}$

Where $5 \theta$ and $4 \theta$ are acute angles

$\Rightarrow \theta=10^{\circ}$

Now we have to find:

$2 \sin 3 \theta-\sqrt{3} \tan 3 \theta$

$=2 \sin 30^{\circ}-\sqrt{3} \tan 30^{\circ}$

$=2 \times \frac{1}{2}-\sqrt{3} \times \frac{1}{\sqrt{3}}$

$=1-1$

$=0$

Hence the correct option is (b)