Sin4x+корень[tex]sin4x+\sqrt{3}cos4x=0[/tex]3cos4x=0

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To solve the equation sin(4x) + sqrt(3)*cos(4x) = 0, we can rewrite it as:

sin(4x) = -sqrt(3)*cos(4x)

Now, divide both sides by cos(4x) to get:

tan(4x) = -sqrt(3)

The solution to this equation can be found by taking the arctangent of both sides:

4x = arctan(-sqrt(3))
4x = -π/3
x = -π/12

So, the solution to the equation sin(4x) + sqrt(3)*cos(4x) = 0 is x = -π/12.