# Sine, Cosine, and Root

Geometry Level 1

If $\sqrt{\sin 5\theta \cos 5\theta}=-\sqrt{\sin 5\theta}\sqrt{\cos 5\theta},$ what is the value of $\sqrt{\tan^2 5\theta}+\sqrt{1-\sin^2 5\theta}-\frac{\sin 5\theta}{\cos 5\theta}-\lvert \cos 5\theta \rvert,$ where $$\sin 5\theta \cos \theta \neq 0?$$

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