Simplifying $ \sqrt{1+\cos\theta}\sqrt{1-\cos\theta} $

geometry trigonometry

Solution 1:

You have\begin{align}\sqrt{1+\cos\theta}\sqrt{1-\cos\theta}&=\sqrt{(1+\cos\theta)(1-\cos\theta)}\\&=\sqrt{1-\cos^2\theta}\\&=\sqrt{\sin^2\theta}\\&=|\sin\theta|.\end{align}

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