If sin θ + sin² θ = 1, then find cos² θ + cos $$^4$$​θ.

Correct option is D

Given:

$$\sin \theta + \sin^2 \theta = 1 \\$$​

Solution:

$$\sin \theta = 1 - \sin^2 \theta \\\sin \theta = \cos^2 \theta \\$$​​
Now, we need to find the value of  $$\cos^2 \theta + \cos ^4\theta \\$$​
From the above, we know $$\cos^2 \theta = \sin \theta \\$$

$$\cos^2 \theta + \cos ^4\theta\\ = \sin \theta + \sin^2 \theta\\= 1$$​​