Is it true that since sin2x+cos2x = 1, then sin (x) + cos (x) = 1? Explain your answer.

Sin2x+cos2x=1

2sinxcosx+2cos^2x-1=1

2cosx (cosx+sinx-1) = 0

2cosx=0 cosx+sinx=1

True

I did this with double angle formulas. sin2x=2sinxcosx, and cos2x=2cos^x-1. With plugging this in, I used factoring. At the end, there are two factors. One of the factors is cosx+sinx-1=0, which is cosx+sinx=1. Therefore, the answer is true.