If sin θ - cos θ = 0 then the value of (sin⁴θ + cos⁴θ) is -------------?

Correct option is A

Given:

If sin θ - cos θ = 0 then the value of (sin⁴θ + cos ⁴θ) is -------------?

Formula used:

sin $$45\degree = \frac{1}{\sqrt{2}}$$

cos $$45\degree = \frac{1}{\sqrt{2}}$$​​

Solution:

sin θ - cos θ = 0

sin θ = cos θ

Hence,

​$$θ = 45\degree$$​​

Therefore.

(sin⁴θ + cos⁴θ)

= $$\sin^4 45^\circ + \cos^4 45^\circ$$​​

= $$\left( \frac{1}{\sqrt{2}} \right)^4 + \left( \frac{1}{\sqrt{2}} \right)^4$$

= $$\frac{1}{4}+\frac{1}{4}$$

= $$\frac{2}{4}$$

= $$\frac{1}{2}$$

Thus, the correct answer is (a).