If $$y \sin 45^\circ \cos 45^\circ = \tan ^245^\circ - \cos^2 30^\circ, \text{ then } y = \ldots$$​​

Correct option is B

Given:  $$y \sin 45^\circ \cos 45^\circ = \tan 2 \cdot 45^\circ - \cos^2 30^\circ$$

Solution:

We know,

​$$\sin 45^\circ = \frac{1}{\sqrt{2}}, \quad \cos 45^\circ = \frac{1}{\sqrt{2}}$$ , $$\tan 45^\circ = 1, \quad \cos 30^\circ = \frac{\sqrt{3}}{2}, \quad$$​​

Now,

$$y \times \frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}} = 1 - \frac{3}{4}$$​​​​

​$$y \times \frac{1}{2} = 1 - \frac{3}{4}$$​​

​$$\frac{y}{2} = \frac{1}{4}$$​​

y = $$\frac{2}{4}$$​

y =$$\frac{1}{2}$$

Thus, the correct answer is (b).