Question

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

Answer 1

True

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))\\eq 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 \\ \\(√(2))/(2)+(√(2))/(2)=1 \\ \\ Rewriting:\\ \\2(√(2))/(2)=1 \\ \\ \therefore √(2)=1 \ FALSE!`

So we observe that the equation is not fulfilled because
`√(2)\\eq 1`. In conclusion:

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