Question

If cos θ + cos²θ = 1, then sin²θ + sin⁴θ = _________.

Answer 1

$$\begin{gathered} \cos \theta +{\cos }^2\theta =1 \\ \Rightarrow \cos \theta =1-{\cos }^2\theta \\ \Rightarrow \cos \theta ={\sin }^2\theta \end{gathered}$$
Squaring on both sides, we get
$$\begin{gathered} {\cos }^2\theta ={\sin }^4\theta \\ \Rightarrow 1-{\sin }^2\theta ={\sin }^4\theta \\ \Rightarrow {\sin }^2\theta +{\sin }^4\theta =1 \end{gathered}$$

If cos θ + cos²θ = 1, then sin²θ + sin⁴θ = ____1_____.