2sin²x-sinxcosx-cos²x=0

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To solve the equation 2sin²x - sinx*cosx - cos²x = 0, we can rewrite it in terms of sinx and cosx:

2(sin²x - cos²x) - sinx*cosx = 0

Using the trigonometric identity sin²x - cos²x = -1, we can simplify the equation further:

2(-1) - sinxcosx = 0
-2 - sinxcosx = 0

Now, we can substitute -sinx*cosx with -sin(2x)/2 (by using the double angle identity for sine) to get:

-2 - sin(2x)/2 = 0
sin(2x) = -4

However, the sine function only takes values between -1 and 1, so there are no solutions to this equation.