Question

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

Answer 1

No it is not true because plugging in something like x = pi/4 radians (equivalent to 45 degrees) leads to the left side not being equal to 1. The left side will simplify to sqrt(2). So the equation is not true when x = pi/4 radians. There are infinitely other counter examples to use; however, x = 0 or x = pi/2 radians will actually be bad values to pick so avoid those.