Question 629319
Method 1: Graph the two expressions (the left and right sides). If they produce two distinct graphs, then they are not the same...which means that the equation is not an identity.


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Method 2: Plug in a specific x value that makes the equation false. This is the easiest and most direct way to prove that the equation is not an identity (and sometimes you don't even need a calculator)


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Method 1:

Graph the left side (in green) and the right side (in blue) using a graphing calculator.


{{{ drawing(500, 500, -5, 15, -10, 10,
 graph( 500, 500, -5, 15, -10, 10,0,sin(2+x),sin(2)+sin(x))

)}}}


Clearly the two graphs are different. So the equation sin(2 + x) = sin 2 + sin x is NOT an identity.


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Method 2:


Plug in any x value (that is NOT a solution to the equation). So let's use the graph to find such a value.


Let's pick x = 10


So 


sin(2 + x) = sin(2) + sin(x)


sin(2 + 10) = sin(2) + sin(10)


sin(12) = sin(2) + sin(10)


0.20791169081776 = 0.0348994967025 + 0.17364817766693 ... Note: I'm in degree mode


0.20791169081776 = 0.20854767436943



The equation above is not true.


So the equation is NOT an identity.


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