Question

Help!
solve for:
sin (pi/4 -x) - sin (x + pi/4) for 0 < x < 2pi

Answer 1

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

`( √(2) )/(2) ( \cos(x) - \sin(x) ) - ( √(2) )/(2) ( \sin(x) + \cos(x) ) = 1 \\ \\ < = > - 2 * ( √(2) )/(2) \sin(x) = 1 \\ \\ < = > \sin(x) = ( - 1)/( √(2) ) \\ \\ < = > x = - (\pi)/(4) + k2\pi \: or \: x = (5\pi)/(4) + k2\pi`

but 0 < x< 2pi => x = { 5pi/4; 7pi/4 }