To solve this trigonometric equation, we can use the double angle formula for cosine:

2cos(x)cos(11π/2) - 2sin(x)sin(11π/2) = sin(x)

Now, we know that cos(11π/2) = cos(6π/2 + 5π/2) = cos(3π) = -1 and sin(11π/2) = sin(6π/2 + 5π/2) = sin(3π) = 0.

So, the equation simplifies to:

-2cos(x) - 0 = sin(x)

Which can be simplified further to:

-2cos(x) = sin(x)

Now, we can square both sides to eliminate the trigonometric functions:

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

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

Using the Pythagorean identity cos^2(x) + sin^2(x) = 1, we can substitute cos^2(x) = 1 - sin^2(x):

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

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

4 = 5sin^2(x)

sin^2(x) = 4/5

Taking the square root of both sides, we get:

sin(x) = ± √(4/5)

Therefore, the solutions to the trigonometric equation are:

sin(x) = √(4/5) or sin(x) = -√(4/5)