Solve for x: sinx-cosx=√2

sinx - cosx = sqrt (2)

Taking square on both sides:

(sinx - cosx) ^2 = sqrt (2) ^2

sin^2 (x) - 2cos (x) sin (x) + cos^2 (x) = 2

Rearranging the equation:

sin^2 (x) + cos^2 (x) - 2cos (x) sin (x) = 2

As,

sin^2 (x) + cos^2 (x) = 1

So,

1-2sinxcosx=2

1-1-2sinxcosx=2-1

- 2sinxcosx = 1

Using Trignometric identities:

-2 (0.5 (sin (x+x) + sin (x-x)) = 1

-sin2x+sin0=1

As,

sin 0 = 0

So,

sin2x+0 = - 1

sin2x = - 1

2x=-90 degrees + t360

Dividing by 2 on both sides:

x=-45 degrees + t180

or 2x=270 degrees + t360

x = 135 degrees + t180 where t is integer