The value of $$\frac{tan⁡85°-tan⁡25°}{(1+tan85°tan⁡25° )}$$​  is:

Correct option is C

Given:

​$$\frac{\tan 85^\circ - \tan 25^\circ}{1 + \tan 85^\circ \cdot \tan 25^\circ}$$​​

Formula Used:

​$$\frac{\tan A - \tan B}{1 + \tan A \cdot \tan B} = \tan (A - B)$$​​

Solution:

​$$\frac{\tan A - \tan B}{1 + \tan A \cdot \tan B} = \tan (A - B)$$​​

​$$\frac{\tan 85^\circ - \tan 25^\circ}{1 + \tan 85^\circ \cdot \tan 25^\circ} = \tan (85^\circ - 25^\circ)$$​​

​$$\tan 60^\circ = \sqrt{3}$$​​

Thus, the value of the given expression =$$\sqrt{3}$$​​