The equation sin(x)=√2/2 is an identity. True or false?

Question

kj4uts · Answer

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anonymous · Answer

its true!

jim_thompson5910 · Answer

An equation is an identity if it is a true equality statement for ALL defined values of the variable(s) in the domain.

jim_thompson5910 · Answer

what's one counter-example if it's false?

kj4uts · Answer

@jim_thompson5910  It is false because an identity means that no matter what value of x we plug in it is always true an example is: 0x = 0 Because you can plug in any single number and it is still true therefore 0x=0 is an identity 
 
For sinx = sqrt2/2 this is not true for every value of x because sin(0) = 0 
 Therefore it is not an identity

jim_thompson5910 · Answer

very good, as long as you can show ONE counterexample, then that disproves the whole claim since EVERY value has to work. By "every" I mean every value in the domain.