<s>[INST] Find $\tan x $ if $\sin x+\cos x=\frac12$ It is given that $0 < x < 180^\circ$ and $\sin x+\cos x=\frac12$, Find $\tan x $. 
I tried all identities I know but I have no idea how to proceed.  Any help would be appreciated. 
 [/INST] Or: $1 + 2\sin{x }\cos{x} = \frac{1}{4},$ so $\sin{x}\cos{x} = \frac{-3}{8},$ leading to $\sin{x} - \cos{x} = \pm \sqrt{ \frac{1}{4} + \frac{3}{2}} = \pm \frac{\sqrt{7}}{2},$ allowing you to solve for $\sin{x}$ and $\cos{x}$ (making use of the fact that $0 < x < \pi$ (radians) so that $\sin{x} >0$).
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