3sin^2x+4cos^2x=13cosx*sinx

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To simplify the equation, we can use the trigonometric identity:

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

Substitute this identity into the equation:

3(1 - cos^2(x)) + 4cos^2(x) = 13sin(x)cos(x)

Expanding the equation:

3 - 3cos^2(x) + 4cos^2(x) = 13sin(x)cos(x)

Combine like terms:

3 + cos^2(x) = 13sin(x)cos(x)

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

3 + cos^2(x) = 13sin(x)cos(x)
3 + cos^2(x) = 13sin(2x)/2

Multiply both sides by 2 to get rid of the fraction:

6 + 2cos^2(x) = 13sin(2x)

At this point, the equation has been simplified as much as possible.