Cosine Sine Equality
If $ 0^\circ < x < 180^\circ $ and $ \cos x + \sin x = \frac{1}{2}, $ then $ \tan x $ can be expressed in the form $ -\frac{a + \sqrt{b}}{c} $ when simplified, where $ a, $ $ b, $ and $ c $ are positive integers. Find $ a + b + c $.
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- +
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- -
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- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$