To solve this equation, we can use the identity for the product of two trigonometric functions:

cos(A)cos(B) - sin(A)sin(B) = cos(A + B)

So in this case, we have:

cos(2x)cos(7x) - sin(2x)sin(7x) = cos(2x + 7x)

cos(2x + 7x) = cos(9x)

Now we have:

cos(9x) = -1

To find the solution, we can see that the cosine function equals -1 at odd multiples of π. Therefore, we can write the general solution as:

9x = (2n + 1)π

where n is an integer.

So, the solution to the equation cos(2x)cos(7x) - sin(2x)sin(7x) = -1 is:

x = (2n + 1)π / 9

where n is an integer.