Prove the following identity:

2 sin x cos x - sin^{2}x - cos^{2}x = 1

For those who have not had Trig, I should tell you that one of the identities is that -sin

^{2}x - cos

^{2}x = -1. Therefore, the above equation could be rewritten as:

2 sin x cos x - 1 = 1

I then simplified the equation further, by adding one to both sides.

2 sin x cos x = 2

From there I went, divided by two, and proved the identity. My problem, according to my teacher, was in the adding of 1 to both sides of the equation. Because the two sides have not been proven to be equal, she said, I cannot add 1 to both sides.

Frankly, this is utter bullshit. If I have the equation 1=2, which is clearly not correct, adding 1 to both sides, yielding 2=3, is also not correct. There is no way that doing something to both sides of an inequality will make them an equality. No possible way.

I guess this is just my way of venting off some anger, but also asking, "What do you think? Should I get those 4 points back, and get that grade up to a 94%?"

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