3cos2x-sin^2 x+cos^2 x=2cos2x

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To simplify this expression, we will first use the fact that 2cos^(2)x - 1 = cos(2x). Multiplying this by 3 gives us:

3(2cos^(2)x - 1) = 6cos^(2)x - 3

Next, we will expand the equation by squaring sin(x) and cos(x):

3cos^(2)x - sin^(2)x + cos^(2)x = 6cos^(2)x - 3

Combining like terms, we get:

3cos^(2)x - sin^(2)x + cos^(2)x = 6cos^(2)x - 3
4cos^(2)x - sin^(2)x = 6cos^(2)x - 3
-sin^(2)x = 2cos^(2)x - 3

Therefore, the simplified equation is:

-sin^(2)x = 2cos^(2)x - 3