​$$\text{If } \sin \theta + \cos \theta = \sqrt{3} \cos(90 - \theta) \text{ then } \tan \theta = ?$$​​

Correct option is B

Given: 

$$\sin\theta+\cos\theta = \sqrt3\cos( 90-\theta)$$ 

Solution:

= $$\sin\theta + \cos\theta = \sqrt3\cos(90^\circ - \theta)$$             (  $$\cos(90^\circ - \theta) = \sin\theta$$  )​

= $$\sin\theta + \cos\theta = \sqrt3\sin\theta$$​​

= $$\frac{\sin\theta}{\sin\theta} + \frac{\cos\theta}{\sin\theta} = \sqrt3$$   

= $$1 + \frac{\cos\theta}{\sin\theta} = \sqrt3$$ 

= $$\frac{\cos\theta}{\sin\theta} = \sqrt3-1$$ 

= $$\frac{\sin\theta}{\cos\theta} = \frac1{\sqrt3-1}$$ 

= $$\tan\theta = \frac1{\sqrt3-1}$$  

Option (b)