3 sin^2 x-3sinx cosx -4 cos^2 x= -2

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To solve this equation, we can rewrite it in terms of sine and cosine:

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

Using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:

3(1 - cos^2(x)) - 3 sin(x) cos(x) - 4 cos^2(x) = -2

Expanding and simplifying the equation gives:

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

Rearranging the terms and combining like terms gives:

-7cos^2(x) - 3 sin(x) cos(x) = -5

Now we can use the trigonometric identity sin(2x) = 2sin(x)cos(x) to simplify the equation further:

-7cos^2(x) - 3 sin(x) cos(x) = -5
-7cos^2(x) - 3 sin(2x) = -5

Now we can solve for cos(x) using the Pythagorean identity cos^2(x) + sin^2(x) = 1:

-7(1 - sin^2(x)) - 3 sin(2x) = -5
-7 + 7sin^2(x) - 3 sin(2x) = -5

Substitute sin(2x) = 2sin(x)cos(x):

-7 + 7sin^2(x) - 6sin(x)cos(x) = -5

Rearrange the equation to solve for sin(x) and cos(x):

7sin^2(x) - 6sin(x)cos(x) = 2

Now we need additional information or constraints to fully solve this equation for sin(x) and cos(x).