If cos theta + cos^2 theta = 1 ,the value of sin^2 theta + sin^4 theta is

Question

If cos θ + cos² θ = 1 ,the value of sin² θ + sin⁴ θ is

Answer 1

cosθ + cos²θ = 1

⇒ 1 - cos²θ = cosθ

⇒ sin²θ = cosθ

Now, sin²θ + sin⁴θ = sin²θ(1 + sin²θ)

= cosθ(1+ cosθ) (∵ sin²θ = cosθ)

= cosθ + cos²θ

= 1.