The value of $$\frac{\sin75^o - \sin15^o}{\cos75^o + \cos15^o}$$ is​

Correct option is C

Given:

​$$\frac{\sin 75^\circ - \sin 15^\circ}{\cos 75^\circ + \cos 15^\circ}$$​​

Formula Used: 

​$$\sin A - \sin B = 2 \cos\left(\frac{A + B}{2}\right) \sin\left(\frac{A - B}{2}\right)$$​​

​$$\cos A + \cos B = 2 \cos\left(\frac{A + B}{2}\right) \cos\left(\frac{A - B}{2}\right)$$ 

Solution:

​$$\frac{\sin 75^\circ - \sin 15^\circ}{\cos 75^\circ + \cos 15^\circ}\\ \ \\= \frac{2 \cos\left(\frac{75^\circ + 15^\circ}{2}\right) \sin\left(\frac{75^\circ - 15^\circ}{2}\right)}{2 \cos\left(\frac{75^\circ + 15^\circ}{2}\right) \cos\left(\frac{75^\circ - 15^\circ}{2}\right)}$$​​

​$$=\frac{2 \cos 45^\circ \sin 30^\circ}{2 \cos 45^\circ \cos 30^\circ}$$​​

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