2) Use the sum and difference identites

Question

sin[x + pi/4] + sin[x-pi/4] = -1

sinx cospi/4 + cosxsin pi/4 + sinx cos pi/4 - cosx sin pi/4 = -1

2 sin x cos pi/4 =-1

cos pi/4 = sqr2/2

2sin^x(sqrt2/2) = -1
sin x = -sqrt2

x = 7pi/4 and 5pi/4

Am I correct?

Answer 1

2sin^x(sqrt2/2) = -1
sin x = -1/sqrt2 = - sqrt 2 /2
x = pi + pi/4 = 5 pi/4
x = 2 pi - pi/4 = 7 pi /4

so I agree with you but you seem to have a typo