If sin θ − cos θ = 0, then the value of sin θ + cos θ is :

1. $\dfrac{1}{\sqrt{2}}$

2. $\sqrt{2}$

3. $\dfrac{1}{4}$

4. $\dfrac{3}{4}$

sin θ = cos θ

Divide both sides by cos θ

$\dfrac{\sin \theta}{\cos \theta} = \dfrac{\cos \theta}{\cos \theta}$

tan θ = 1

For acute angles, tan θ = 1 when θ = 45°.

⇒ sin 45° + cos 45°

$\dfrac{1}{\sqrt2} + \dfrac{1}{\sqrt2}$

⇒ $\dfrac{2}{\sqrt2}$

⇒ $\sqrt2$

Hence, option 2 is the correct option.