If tanα = $$\frac{1}{\text{x}}$$​, then find the value of sinα + cosα.

Correct option is C

Given:

​$$\tan \alpha = \frac{1}{x}$$​​

Formula Used:

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

​$$(\sin \alpha + \cos \alpha)^2 = 1 + 2 \sin \alpha \cos \alpha$$​​

Solution:
From $$\tan \alpha = \frac{1}{x}$$​, we know that:

​$$\frac{\sin \alpha}{\cos \alpha} = \frac{1}{x}$$​​

This implies:

​$$\sin \alpha = \frac{1}{x} \cos \alpha$$​​

Substitute this into the Pythagorean identity $$\sin^2 \alpha + \cos^2 \alpha = 1$$​:

​Alternate Solution:  

​$$\tan \alpha = \frac{1}{x}$$  

Thus:

​$$\sin \alpha = \frac{1}{\sqrt{x^2 + 1}}, \quad \cos \alpha = \frac{x}{\sqrt{x^2 + 1}}$$  

Now, 

​$$\sin \alpha + \cos \alpha = \frac{1}{\sqrt{x^2 + 1}} + \frac{x}{\sqrt{x^2 + 1}} = \frac{1 + x}{\sqrt{x^2 + 1}}$$ ​