If sin θ − cos θ = 0, then the value of (sin⁴ θ + cos⁴ θ) is :

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

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

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

4. 1

⇒ sin θ − cos θ = 0

⇒ sin θ = cos θ

Divide by cos θ

⇒ $\dfrac{sin \theta}{\cos \theta}$ = 1

tan 45° = 1

Given expression,

(sin⁴ 45° + cos⁴ 45°)

$\Rightarrow \Big(\dfrac{1}{\sqrt2}\Big)^4 + \Big(\dfrac{1}{\sqrt2}\Big)^4 \\[1em] \Rightarrow \Big(\dfrac{1}{4}\Big) + \Big(\dfrac{1}{4}\Big) \\[1em] \Rightarrow \dfrac{1}{2}.$

Hence, option 2 is the correct option.