MHB Use double or half angle formulas

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The discussion focuses on applying double angle formulas to the equation cos(2*theta) + sin^2 = 0. The relevant double-angle formula for cosine is identified as cos(2*theta) = cos^2(theta) - sin^2(theta). By substituting this into the equation, it simplifies to cos^2(theta) = 0. The conversation seeks further insights on solving for theta from this equation. Overall, the use of double angle formulas is emphasized as a key step in solving trigonometric problems.
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Ok, So with this problem it says to use double angle or half angle formula. I have the formulas in my notes just not sure how to apply them to the problem I feel like I should be using the double formula though. Here's the problem:

cos(2*theta)+sin^2=0
 
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Yes the double-angle formula for $\cos$ would be useful. There are a few different forms but consider that $\cos (2 \theta) = \cos^2 (\theta) - \sin^2 (\theta)$. Substituting in we get,

$\cos^2 (\theta) - \sin^2 (\theta) + \sin^2 (\theta) = \cos^2 (\theta) = 0$.

Do you have any ideas on how to solve for $\theta$?
 
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