3sin^2x+3sinxcosx+2cos^2x=1

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To simplify the given expression, we can use the trigonometric identity:

sin^2(x) + cos^2(x) = 1

We can rearrange the given expression by applying this identity:

3sin^2(x) + 3sin(x)cos(x) + 2cos^2(x) = 1
3(sin^2(x) + 2sin(x)cos(x) + cos^2(x)) = 1
3(sin(x) + cos(x))^2 = 1

Taking the square root of both sides:

sin(x) + cos(x) = ±1/√3

Therefore, the simplified expression is:

sin(x) + cos(x) = ±1/√3