Question

Is it true that since sin^2(x) + cos^2(x)=1, then sin(x) + cos(x) = 1? Explain

Answer 1

No it is not true because the 2 expressions are not equal nor is sin^2 x + cos^2 x equal to the square of sin x + cos x.

Answer 2

No.

An easy counterexample is sin(30°) + cos(30°) which is more than 1.