If $$\sin \theta - \sqrt3 \cos \theta = 0$$ ($$\theta$$​ is an acute angle), then the value of $$\sin^2\theta - \cos^2 \theta$$ is:

Given: 

​$$\sin \theta - \sqrt 3\cos \theta = 0$$ 

To find: Value of $$\sin^2 \theta - \cos^2 \theta$$ 

Formula Used: 

​$$\ \frac{\sin \theta}{\cos \theta} = \tan \theta$$   

Solution: 

​$$\sin \theta - \sqrt3 \cos \theta = 0 \\ \sin \theta = \sqrt3 \cos \theta \\ \frac{\sin \theta}{\cos \theta} = \sqrt3 \\ \tan \theta = \sqrt3 \\ \implies \theta = 60^\circ$$ 

Putting the value of $$\theta = 60^\circ$$ 

$$=\sin^2 60^\circ - \cos^2 60^\circ \\ =\left(\frac{\sqrt3}{2}\right)^2 - \left(\frac{1}{2}\right)^2 \\ \ \\ = \frac{3}{4} - \frac{1}{4} \\ \ \\ =\bf \frac{1}{2}$$​​​​