Question 872509
Find all solutions of the equation in the interval [0, 2π)
solve for x 
{{{sin(x + pi/4)- sin(x - 5pi/4) = sqrt(2)/2}}}
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{{{sin(x+pi/4)=sinx*cos(pi/4)+cosx*sin(pi/4)}}}
{{{sin(x+pi/4)=sinx*(sqrt(2)/2)+cosx*(sqrt(2)/2)=(sqrt(2)/2)(sinx+cosx))}}}
...
{{{sin(x-5pi/4)=sinx*cos(5pi/4)-cosx*sin(5pi/4)}}}
{{{sin(x-5pi/4)=sinx*(-sqrt(2)/2)-cosx*(-sqrt(2)/2)=(-sqrt(2)/2)(sinx-cosx)}}}
...
{{{sin(x + pi/4)- sin(x - 5pi/4) =(sqrt(2)/2)(sinx+cosx)-(-sqrt(2)/2)(sinx-cosx)}}}
{{{(sqrt(2)/2)(sinx+cosx)+(sqrt(2)/2)(sinx-cosx)=(sqrt(2)/2)((sinx+cosx)+(sinx-cosx))
=(sqrt(2)/2)(2sinx)=sqrt(2)sinx)}}}
...
{{{sqrt(2)sinx=sqrt(2)/2}}}
{{{sinx=1/2}}}
x=π/6, 5π/6