For this case we have the following expression:
sin (x) + cos (x) = 1
Substituting x = 45 degrees we have:
sin (45) + cos (45) = 1
(root (2) / 2) + (root (2) / 2) = 1
Rewriting:
(root (2) + root (2)) / 2 = 1
(2 * root (2)) / 2 = 1
root (2) = 1
We observe that the equation is not fulfilled.
Answer:
Yes, A counterexample for the expression sin (x) + cos (x) = 1 is 45 °.
TRUE
