3cos²x+sinx cosx=2sin²x

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To solve for x, we can rewrite this equation in terms of sine and cosine using the identity cos^2(x) = 1 - sin^2(x):

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

Expanding the left side and simplifying the equation gives:

3 - 3sin^2(x) + sin(x)cos(x) = 2sin^2(x)
3 - 3sin^2(x) + sin(x)cos(x) - 2sin^2(x) = 0
3 - 5sin^2(x) + sin(x)cos(x) = 0

Now, we can use the double angle identity sin(2x) = 2sin(x)cos(x) to rewrite the equation:

3 - 5sin^2(x) + sin(2x) = 0

At this point, the equation is not easily solvable algebraically. However, you can input this equation into a graphing calculator or solve numerically to find approximate solutions for x.