SOLUTION: Can you please describe two methods that you could use to show that sin(2 + x) = sin 2 + sin x is not an identity. Then use those methods to show that it is not an identity. Thanks

Question 629319: Can you please describe two methods that you could use to show that sin(2 + x) = sin 2 + sin x is not an identity. Then use those methods to show that it is not an identity. Thanks! : )
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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.

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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Jim
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