2sinxcosx-2sinx-cosx+1=0

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To solve this equation, we can rewrite it as:

2sinx*cosx - 2sinx - cosx + 1 = 0

Now, let's factor out a sinx from the first two terms and a -1 from the last two terms:

sinx(2cosx - 2) - 1(cosx - 1) = 0

Now, we can factor out a 2 from the first term inside the parentheses:

2sinx(cosx - 1) - (cosx - 1) = 0

Now we have a common factor of (cosx - 1) that we can factor out:

(cosx - 1)(2sinx - 1) = 0

Now we have two possible solutions for cosx - 1 = 0 and 2sinx - 1 = 0:

cosx = 1
2sinx = 1

The solutions for cosx = 1 are x = 0 and x = 2π, and the solution for 2sinx = 1 is x = π/6.

Therefore, the solutions to the equation 2sinxcosx - 2sinx - cosx + 1 = 0 are x = 0, x = π/6, and x = 2π.