If Sinθ+sin²θ=1 Prove that cos²θ+Sin⁴θ=1

Question

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Answer 1

This is impossible because it isn't true. 

 

Let me give a counter example that disproves the statement:

 

If you solve sin(θ)+sin²(θ) = 1, one of the many possible answers is 38.173°. 

 

If you plug that angle into the second equation, you get:

 

cos²(38.173)+sin⁴(38.173) = 0.764 ≠ 1

 

Therefore the statement is false. 

 

Are you certain the original question isn't this?

 

If sinθ+sin²θ=1, prove that cos²θ+cos⁴θ=1. This is actually provable.