SOLUTION: Find the exact values of all solutions in the interval 0<x<2pi for sin(x+(pi/4))+sin(x-(pi/4))=-1

               sin(x + ) + sin(x - ) = -1

sin(x)cos() + cos(x)sin() + sin(x)cos() - cos(x)sin() = -1

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

               2sin(x)cos() = -1

               sin(x)cos() = 

and since cos() = 

               sin(x)· = 

Multiply both sides by 2

               sin(x)·√2 = -1

               sin(x) = 

               sin(x) = ·

               sin(x) = 

               x = ,  

Edwin