Is this correct?
(sinx - cosx)^2 = 1 - 2sinxcosx
LS = sin^2x - 2sinxcosx + cos^2x
= 1 - cos^2x - 2sinxcosx + cos^2x
= 1 - cos^2x + cos^2x - 2sinxcosx
= 1 - 2sinxcosx
LS = RS
Yes, the equation (sinx - cosx)^2 = 1 - 2sinxcosx is correct. To verify this, let's expand both sides of the equation and simplify.
Starting with the left side (LS):
(LS) = (sinx - cosx)^2
= (sinx - cosx)(sinx - cosx)
= sin^2x - sinxcosx - cosxsinx + cos^2x
= sin^2x - 2sinxcosx + cos^2x
Now, let's simplify the right side (RS):
(RS) = 1 - 2sinxcosx
Comparing LS and RS, we can see that they are equal:
LS = RS
sin^2x - 2sinxcosx + cos^2x = 1 - 2sinxcosx
Therefore, the statement is correct.