2cos4x-4sin(п/2+2x)+3=0

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To solve this equation, we will first use the trigonometric identity:

sin(π/2 + θ) = cos(θ)

Substitute sin(π/2 + 2x) with cos(2x) in the equation:

2cos(4x) - 4cos(2x) + 3 = 0

Next, we will use the double angle formula for cosine:

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

Substitute cos(2x) with 2cos^2(x) - 1 in the equation:

2cos(4x) - 4(2cos^2(x) - 1) + 3 = 0

Simplify the equation:

2cos(4x) - 8cos^2(x) + 4 + 3 = 0
2cos(4x) - 8cos^2(x) + 7 = 0

Now, we have a quadratic equation in terms of cosine:

8cos^2(x) - 2cos(4x) + 7 = 0

Solving this equation for cos(x) will give you the solutions for x.