Question

Sin - cos = - radical 2

I don't understand this. It wants you to make the right side equal to zero and solve

Answer 1

sinx - cosx = √2
square both sides and you have
sin^2x - 2sinx cosx + cos^2x = 2
-2sinx cos x = 1
sin 2x = -1
2x = 3pi/2
x = 3pi/4

Or, note that

sinx - cosx
= √2 (sinx * 1/√2 - cosx * 1/√2)
= √2 sin(x - pi/4)
so,
√2 sin(x-pi/4) = √2
sin(x-pi/4) = 1
x - pi/4 = pi/2
x = 3pi/4

Answer 2

I see that I missed the fact that it was -√2 on the right. Just make the fix and redo the calculations to find that x = 7pi/4

Answer 3

If - radical 2 is squared wouldn't it still turn out to be positive 2?