Question 773421
<pre>

               sin(x + {{{pi/4}}}) + sin(x - {{{pi/4}}}) = -1

sin(x)cos({{{pi/4}}}) + cos(x)sin({{{pi/4}}}) + sin(x)cos({{{pi/4}}}) - cos(x)sin({{{pi/4}}}) = -1

2nd and 4th terms on the left cancel, 1st and 3rd terms are the same:

               2sin(x)cos({{{pi/4}}}) = -1

               sin(x)cos({{{pi/4}}}) = {{{-1/2}}}

and since cos({{{pi/4}}}) = {{{sqrt(2)/2}}}

               sin(x)·{{{sqrt(2)/2}}} = {{{-1/2}}}

Multiply both sides by 2

               sin(x)·&#8730;<span style="text-decoration: overline">2</span> = -1

               sin(x) = {{{-1/(sqrt(2))}}}

               sin(x) = {{{-1/(sqrt(2))}}}·{{{sqrt(2)/sqrt(2)}}}

               sin(x) = {{{-sqrt(2)/2}}}

               x = {{{5pi/4}}}, {{{7pi/4}}} 

Edwin</pre>