SOLUTION: Given: {{{sin(theta)-cos(theta)=1/2}}} Prove: {{{sin(theta)+cos(theta)=("" +- sqrt(7))/2}}}

Square both sides



































That's the proof.

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Notice that the right side could be either positive or negative,
although you did not have the ± originally.  I included it above).

To show that it can  be either positive or negative:

By calculator the solutions between 0° and 360° are approximately

 and 

and 

For 



and for ,



So you see that it can be positive or negative.

Edwin