We are given the equation:
sin θ + sin² θ = 1.

We need to find the value of cos² θ + cos⁴ θ.

Step 1: Express sin² θ in terms of sin θ
Rearrange the given equation:
sin² θ = 1 – sin θ.

Step 2: Use the Pythagorean identity
From the Pythagorean identity, we know:
sin² θ + cos² θ = 1.

Substitute sin² θ = 1 – sin θ into the identity:
(1 – sin θ) + cos² θ = 1.

Simplify:
cos² θ = sin θ.

Step 3: Express cos⁴ θ in terms of cos² θ
Since cos² θ = sin θ, we can write:
cos⁴ θ = (cos² θ)² = (sin θ)² = sin² θ.

Step 4: Substitute into cos² θ + cos⁴ θ
Now substitute cos² θ = sin θ and cos⁴ θ = sin² θ into the expression cos² θ + cos⁴ θ:
cos² θ + cos⁴ θ = sin θ + sin² θ.

From the given equation, we know:
sin θ + sin² θ = 1.

Thus:
cos² θ + cos⁴ θ = 1.
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.

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