(cos^2(2x+п/6)-3/4)sinx/2=0

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To solve this equation, we can first rewrite the expression in terms of trigonometric identities:

cos^2(2x + π/6) - 3/4 = 0

Using the identity cos(2θ) = 2cos^2(θ) - 1, we can rewrite cos^2(2x + π/6):

2cos^2(2x + π/6) - 1 - 3/4 = 0
2cos^2(2x + π/6) - 7/4 = 0

Now, we can use the identity sin(2θ) = 2sin(θ)cos(θ) to rewrite sin(x/2):

sin(x/2) = 2sin(x/4)cos(x/4)

Substitute this into the equation above:

2cos^2(2x + π/6) - 7/4 = 0
2(2sin(x/4)cos(x/4))^2 - 7/4 = 0
2sin^2(x/4)cos^2(x/4) - 7/4 = 0
sin^2(x/4)cos^2(x/4) = 7/8

Now we have a trigonometric equation involving both sine and cosine terms. This equation can be further simplified using trigonometric identities, but it may not have an exact solution. We can use numerical methods or graphs to approximate the solutions.