Question

If cos θ + cos² θ = 1, then sin² θ + sin⁴ θ = ______.

Answer 1

If cos θ + cos² θ = 1, then sin² θ + sin⁴ θ = 1.

Explanation:

Let x = cos θ.

From x + x² = 1 we get x² = 1 – x. 

Then sin² θ = 1 – cos² θ = 1 – x²

= 1 – (1 – x)

= x

So sin⁴ θ = x². 

Hence sin² θ + sin⁴ θ = x + x²

= cos θ + cos² θ

= 1