Assertion (A): If sin 2 A + sin A = 1 then cos 4 A + cos 2 A = 1.

Given,

⇒ sin² A + sin A = 1

⇒ sin A = 1 - sin² A

⇒ sin A = cos² A

Squaring both the sides, we get :

⇒ (sin A)² = (cos² A)²

⇒ sin² A = cos⁴ A ......................(1)

Solving L.H.S. of cos⁴ A + cos² A = 1, we get :

⇒ cos⁴ A + cos² A

⇒ sin² A + cos² A [From equation (1)]

⇒ 1.

Since, L.H.S. = R.H.S.

∴ Assertion (A) is true.

As we know that, sin² A + cos² A = 1

⇒ 1 - sin² A = cos² A

∴ Reason (R) is true.

∴ Both (A) and (R) are true, and (R) is the correct reason for (A).

Hence, option 3 is the correct option.