Question

A counterexample for the expression sinx+cosx=1 is 45 degrees T or F

Answer 1

Answer:

True

Step-by-step explanation:

A counterexample is a special type of example that is an exception to a general rule, law, proposition or statement. Hence if we prove that $sin(45^{\circ})+cos(45^{\circ})\neq 1$ then this is a counterexample for the expression $sin(x)+cos(x)=1$. Thus:

$sin(x)+cos(x)=1 \\ \\ Substituting \ x=45^{\circ} \ we \ have: \\ \\ sin(45^{\circ})+cos(45^{\circ})=1 \\ \\\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}=1 \\ \\ Rewriting:\\ \\2\frac{\sqrt{2}}{2}=1 \\ \\ \therefore \sqrt{2}=1 \ FALSE!$

So we observe that the equation is not fulfilled because $\sqrt{2}\neq 1$. In conclusion:

A counterexample for the expression sin(x)+cos(x)=1 is 45° is true!