8sin*x/2*cos*x/2*cos*x*cos2x=1

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To solve this equation, we need to simplify the expression first:

8sin(x/2)cos(x/2)cos(x)cos(2x) = 1

Next, we can apply double angle formulas to simplify cos(2x):

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

Therefore, the equation becomes:

8sin(x/2)cos(x/2)cos(x)(2cos^2(x) - 1) = 1

Now, let's expand the expression and simplify:

16sin(x/2)cos(x/2)cos(x)cos^2(x) - 8sin(x/2)cos(x/2)cos(x) = 1

Now, we can substitute sin(x/2)cos(x/2) with (1/2)sin(x) due to the double angle formula:

8(1/2)sin(x)cos(x)cos^2(x) - 4(1/2)sin(x)cos(x) = 1

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

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

Now, substitute cos(2x) = 2cos^2(x) - 1:

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

Now we can apply the double angle formula for sine:

sin(2x) = 2sin(x)cos(x)

Therefore, the equation simplifies to:

2sin(2x) = 1

Finally, solving for x:

sin(2x) = 1/2
2x = π/6 + 2nπ and 2x = 5π/6 + 2nπ
x = π/12 + nπ and x = 5π/12 + nπ, where n is an integer.